Observations on Reversionary Payments: On Schemes for Providing Annuities ...

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1

OBSE RV

O

REVERSIONAR

Schemes forprov:

forWjDows,andfor

o

The Method of Cal

of AssuRANc:

AND

The

NATIO

To which

F O

U R I

On different Subjcfts in
Annuities and Poli

A» APPENDIX A»

Containing additional Obfe
ofTABLBS; particular);
Probabilities or Life in
the Values of Annuities c

The THIRP EDIT]
By RICHARD P-]

L N
Printed for T. C A B

7 ;«r~--*-

>^

'S ^<» "M V.

if"*!

v;

•'*!

I

TO

>

iThv Rioht Honourable

THE

Rt of SHELBURNE,

T H J S WO RK is,

yrT0x all Gratitude and Respect,

I If S C It I B E 9,

8y

His Lordship *8

Moft obliged, and
Moft obedient humble Servant,

Richard Pricz.

• t

%

^ '^\

t •

t r 1

• • •

C ON TENTS.

•

I

P

RE PACE to the Fir ft Edition Page i* ^
Preface to the - ^bird Edition p. x vii

C tt A P. L

Sluejiidns relating to Schemes for granting Re-^

ver^fionary Annuities^ and the Values ofAf^

Jurances on Lites «^ !*^ . P* I

CHAP, ih

Secti 1. O/' the London Annuity, and
Laudable Societies for the Ben^t of Widows^

Sect. II. Of the AJfotiation among the Lon-
don Clergy dhd the Minifiers in Scotland,
for providing Annuities for their Widows^

p. 84

Sect. IIL Of the befi Schemes for provide

ing Annuities for Widows. -»— p* 95

Sect. IV. Of Schemes fot providing Life^

Annuities^ npbichnrenot to commence 'tilt

particular Ages ; andy particularly i of the

I ' Societies lately cjtablifhed in Loridoiiyir thi

' Benefit of Old Age. *-- . *— p. 106

a 3 SscT^j

Yi CO NT ^^ r s.

Sect. V. ty/^^ Amicable Corporation y2r
a perpetual Affurance^OMce : and the So^
ciety for Equitable Amirances on Lives
1^ SqrvivorihipsV — — - p. 120

CHAP. III.
Of Public Credit, and the Nationai Debt.

E S S A Y L

Obfervations on the l^peSlations of Lives ; the
Increqfe of Mankinds the Number oflnba^
titahts in^, Lopdoa ; and the Infkience of
gr^at Toivni on Health and Population.
Jn a Letter to Benjamin Franklin, Efqi
L. L. D. and F. R. S. p. 167* To which
is added, a P^Jcr^t, containing Obferva^^
tions on Edinburgh, Paris, and Berlin*

p. 213

ESSAY 11.

On Mr. De MoivreV Rules for calculating tbt
Values of ]Qmt Lives ^ — p. 3^27

ESSAY III.

On the Method of calculating thh Values ifRe-^
verfons depending on Sufvivorjloips. p. 233

E S S A y IV.

On the proper Method of conJlruSing Tables
for determining the Rate of human Morta^

J

• ■• "»

C O N T E NT $• ^ii

iky 9 the Number of Inhabitants ^ and the

Values of Lives in any Town or DiJlHiSf,

from Bills of Mortality in tvbich are given

ibe Numbers dying annually at all Ages.

p. 240

Appendix.

tlonidihing Algebraical Demonf rations iTablesi
and Rules for computing the Increafe of
Money bearing compound Intereft. p. 28 j

SUPPLEMENT. ^

Containing additional Obfervations and tables.

P- 357

^

a 4 IPui-'

i

\ »

Pui/i/beJ hy the fame Author^
For T. C A iJ k L L, in the Stf and,

• • • * *

I. A Review of the principal Queftions and
£\ Difficulcies in Morals. Particularly,
thofc relating to the Original of our Ideas of Vir-
tue, its Nature, Foundation, Reference to the
Deity, Obligation, Subjedi-niattcr, and San&ions.
The Second Edition corrcftcd, 6 s.

II. Fqur Dissertations.— —I. On Provi-
dence. II. On Prayer, III. On the Rea-

fons for expedling that virtuous Men (hall meet

after Death in a State of Happinefs. IV. On

the Importance of Chriftianity, the Nature of Hi-
ftorical , Evidence, and Miracles. The Third
Edition, with Additions, 6 s.

III. An Appeg^l to the Public on the Subjeft of
the National Debt. The Second Edition, with an
Appendix, containing explanatory Oblervations
and Tables, and an Account of the prefent State
of Population in Norfolk. Price 2 Si*

Pre-

t « ]

>x*x#x4>x^xf«>t><:^x*x*x*x*x

PREFACE to the First Edition.

BEFORE the Reader enters upon this
Work, it will not be improper to give
him the following information concerning it.
. A few years ago, many gentlemen, of the
firft eminence in the law, formed themfelves
into a Society^ for providing anquities for the
widows of all fuch perfons in judicial offices,
barriflers, civilians^ and folicitors, as ihould
chufe to become members. A plan was agreed
upon and printed ; but, fome doubts happen-
ing to arife with refpedl to it, the diredors
refolyed to aik the opinion and advice of thr^ee
gentlemen, well known for their fkill in cal-
culation. This occaiioned a further reference
to me ;^ and the ifTue was, that the plan bc->
ing found to be infufficient, the whole defiga
was laid afide.

About the fame time, feveral other focic-

ties were formed with the fame views ; but

all on plans alike improper and infufEcient*

Finding, therefore^ that the public wanted

7 infpr-

f PtLErAicn to iBe

i

information oh this fbbjeift; I was led to un«
dertakd this work j imagining; that it might
1^ fooix finiflied; and that all I could fay
might be brought into a veiy narrow com-
pafs. But in this I have been much miilakeh;.
A defign^ which I at iirft thotight would
give little trouble^ has carried me fai- into a
very wide field of enquiry j and engaged me
in many calculations that have taken up liifieh
time and labour. - I fhall^ however^ be fuffi-
ciently rewarded for my labour, fhould it
prove the means of preventing any part of
that diftrefs, which is likely to be hereafter
produced by the focieties now fubfifHng for
the benefit of widows. ■■ I have proved the
inade^atenefs of their plans, by undeniable
fads and mathematical demonftratii)n;~-f
have, further, given an account of fome of
the beft plansj that are confiftent with a fuf--^
ficient probability of permanency and fuc-
cefs.—-— Should, therefore, any of thefe fo-
cieties determine to reform themfelves ; or
ihould any inftitutions of the fame kind be
hereafter eftablilhed, they will here find di-»

re&ion and 'aiiiftance(^)«

lit

(a) I have Utely learnt, that Mr, Catklly the publiflier
of this work, an^ aUb Mr. B$fht^ Bookfelkr in tba

Strand^

1

F I K S T B J) I T- 1 O Nrf tl

«

In Q^ieftion VL Chap. I. a general me^
^4 ^ 4^cribed of finding the valu^^* io;

■

S&andj arc commiffioned to deliver in Lmdw^ printed
accounts of the fcheme of a focietj, eftablHhed five
jfiact ago at; Jhnfltrdafih for granting annuities on furvi-*
vorQiip.-— I cannot .fatisfy my own mind without intro*
ducing here, 'though an improper place, the fo!Iowing
lemarks on this fct^mf •

^ From the folution of Queftions L and IV. in the Firft
Chapter of the following Work, it may be gathered, that,
(recI(oning intereft at 34 /rr a^t. and the probabilities of.
life as they dre in Tables III. IV.. and V. in the ^r
pi9uBx) the value of an annuity of i /. for life,* to be en^
joyed by a perfoa a^ed ao,' provided he furvives aDotbcr
perfgn aged 60, is S/. 16 s. bd, in qne prefent patyment ^
sMod i8i. 6d. in annual pavments, durms the two joint*
lives : the firft payment to be made immediately* Aftt^.
p4munty therefore, of 130 fiorins^ entitlej^ to an annuity
w \^fiortm\ and an tTn/iir^A payment of iiojhrim^ to an
annuity of 11^ florins i and both together, to an annuity,
of iT^flori/is. If the annual payments are to be made, not,
during the joint lives, but during the whole continuance
0/ tho oldtn^gle life, they will, together. with the ftngle
payment, entitle to an annuity of 144 fiorlm. But this
ibciety promifes, for thefe payments, an annuity of 100
jkrinty if the oMeft lifs fails in the firft year after admif-
fion } 200 florins, if it fails in the 2d year ; yooflorinSf if
it fuis in tne third ; ^00 florins^ if it fails in the 4th ; and
500 florins f if it faib in the fifth year, or at any time af*
terwards. It is, therefore, evident that the fcheme of
this fociety is, in this inftance, grofsly dekikive. There
are other inftances in which it is even more defsAive ;
and the wboU of it, like the fchemes of moft of the Lom^
don focieties, appears to have been contrived by peribns
^bo had no principles to go upon. And yet it has beeii
much encouraged. Many have entered themfelves into
it from different parts of Europf, and the printed'plan
acquaints us, that it is now in pofleffion of an annual in--

come

«

Jf?f^le and'ah/inaf Y>^ymcnts, of all Iifc-anhtil-
tics which are to begin after a given ternt
of years ; and, in the 4th Se<Slion of the 2d
Chapter, the plans of the focieties for grant-
ing fuch annuities are particularly confideredj
and proved to be extremely deficient."-^—*
Indeed, the general difpofition which has
lately (hewn itfelf to encourage thefe focieties,
is a matter of the moil ferious concern 1 and
ought, I think, to be takcA undet the ho*
tice of the Legiilature. The leading perfon$
among xS\z frefent members, will be thejirji
annuitants s and they are fure of being
gainers : and the moreinfofficient the fcheme
is, on which a fociety i^ formed, the greater
will be the gains of the lirft annuitants*
The fame principle, therefore, that has pro-
duced and kept up other bubbles^ has a ten-
come of zoo^ooo florins. What dirappointment then muil
it in time produce?-— ^It is provided by its rules, that
the terms of admiffion fhall become lefs and lefs advan- .
tageous, the longer it has fubfifted ; juft as if the value
of the annuities it prom ifes. depended, not on the proba-
bilities of life, and the improvement to be made of mo-
ney, but on the age of the fociety.— — I have taken no*
tice of a fimilar abfurdity in the rules of our own focie-
ties. But it is eafy to fee what is meant by it.

lAv. Cadell can procure from his correfpondents . in
Holland^ any information for thofe who may want u^
know more of this fociety. But indeed I (hould be forry
to find it much enquired after in LoNpoN*

dcncy

Fix ST Editfon. xii£

m ■

de^y to preierve wd- pipmotf^- tb^fe ; tn<l>
for; jtbis r^afoo> it is to be fearec^ th^t, in. tl^
pr^qnt cafe, no argument^ will bip* attexidqcl
with .any efied. ^The confidcration^ tW
/* . the gain ma4c by focne in tliuefc focietios^
.<* will hp fo much plunder ^taken froin
J^ others^" o^Mght irnpiediately to engage, all
^^^'ijt^tbdraw ftopi^bw^ have any regard

,^.: juftice . ^d hunjanilyi but experience
^pt^X^h (that this. argumeptj when.oppo/ed^<o
pnvfttp int?rcft,. is apt tP.be too fecWe in its

It cannot be faid with precifioQi how long
thefe ibcieties ra^y cpntinup thtii payments
,to anpuitantSj after beginning them. A con*
tinujsd increafe^ and a great proportion joif
'^qung member^, may fpppprttliem for a
loi^ger timQ thaiv | ^an foresee. But the
longer they ar9 Supported by fuch means^ the
Vppre mifchief they muft oc(:afibn.— So, a
tiradefman^ who., fells cheaper than /he buys^
niay be kept, up • many years by increafing
bufinefs and credit j but be will be all the
wl^ile accumulating diftrefs ; and the longer
l^e goes on, the more extenfivf ruin he will
"produce at laft. .

In

*
In the latteh thd dF Ae iifft Chapter, t

liave ftat!6d ^eiy particularly, the method of
]toroputipg jthe values of affkrahces on livie
'^d furvivorihips, iii ;dl cafes whert no mo/e
than Wo Yi^ti are €X)ncerned : ihd, ih tiie
3d Etfajr, )[ hiive pointed 6ufc isi cohfidibrabte
itror, into Which |nfit?i ii dkiigei- of ^fin'gta
'computing fotne of ^efe valuei. Th/i ra-
cletiefi 4tld of)icei for tnihradin^ blifindTsik
itfais way, iti^e Very iifefut; and it is iliec((i&l^

th^t they rhdtiid go tipon Ihtf^jsft pfind^li^^
and poiTefs all the information th^i caQ d6
ftivfen thetti. . ~ . . '

But tKc^e i's tlo t>irt of this WtiffetA V^hiih
the public is fo riiuch concerhcd, as the 3d
Chapter, , It will be there 6rbved, that liad
the Turns rdiild for public ' fefvices iirite ti^
RevolIjtIon, been inilchgrtater tjian the^
have fcieen,!thi increafe of thfc publie debti?
to tljeir pf fel^ht ftit^ might have been jprcV
rented in th<^ ci^fieft mliihfer, dnd ^i a tricing
^xpence. A metnodi liMwiiei bfiedu^iiig
within d,u4 b6ufids thpffeldebtS, heavy as^lhey
ipaw are, <vill be pf6poied.-r-All cbrnpefeht
judges Will, I believe, fee, that this met^o^^
being founded on the moft perfed improve^
ment that can be made of money, is the mof(

expc?

■

l^peditioQS and tfk&usl that the natures of
things admit of. Nor^ in my opinion^ if tbp
nation h not yet too near the limit of its ret-
fourpef , can thcf e be any good reafon againft
carrying it into execution. — ~- It is wtdl
knowni to yrhtt prodigious fums, mone^^
improved for finnft time at comp^uni inurtfi^
will increafe ( j). A ftate^ if there is no mif^
fif^lication of mcfiey» ihuft neceflarily make
this improvement of any fayings^ v^hich can
|)e applied to the payment of its debts. It
yieed never, therefore, be under any difficul-
ties ; for, with xSxtfmalleft favings, it may, in
as little? time as ita intereil can require, pay
oflf the largefi debts.

In iiitjfrji EiTay I have made mapy obfei;«
yations on the expedations of lives, the per*
picious influence of great towns on health.

« f I • •

%% i . . ^: ■ • . . . . ►. i i • .: : * ■ » i

{a) A finrvfy fo imptx)ved from our Saviour's birth, as
to aotibk itfcl'f cveiy 14 years, W, Which is nearly the
iane, piit out to 5 fir cent, compound intereft at our
$aviQur's birth, would, by this time, have increafed to
fiiore ftioney than would be contained in 150 millions
6f globes, eiich equaf to the earth in magnitude, and all
folid gold. A Jhillittgj put out to 6 per cent, compound
intereft, would, in the fame time, have increafed to ai
greater Aim ihj^old than the vfho\e folarjji/lem could hold,
fuppoilng it a ^here equal in'diamet^r to the diameter of
Saturn'^ orbit. And the earth is tofuch a fphere, nearly
as half 2, fquare foot> or a quarto page, to the whole fur-^
face of the earth*

anQ|

:ftrL P Ji E F A c E, &c.

and mannersj and population j the intrreafeqf
mankind r and other, fubjed^ in the dodbrilip
of Annuities and Political: Arithmetic^——
Jn the Lafl; EiTay I have ftated carefully the
proper method of forming Tables of thie pror
babilities of human lif<^» from given ob&rva-
tions : And> in the Appendix^ befides feveral
new Tables^ I have thought it neceflary. to
give Mr. Simp/on' s Tables of the values and
expedation$ of Lonpon lives ; and all the
other Tables which can be wanted an the
perufal of this work.— -I have alfo, in the
Appendix, given the Demonftrations of the
Anfwers to the Sl^ejiions in Chap, I. Thefc
Demonftrations I have chofen to keep out. of
fight in the body of the work, in order to
avoid difcouraging fuch readers as may be
unacquainted with mathematics*

Upon the whole. A great part of this
work is, I believe, new ; and I am in hope^
alfo, that it will be found to contain fome
improvements ' in thofe branches of philofo*
phical enquiry, which are the fubjefts of it.

PRE

f • xvii 3

i©if<2Nje^.<«>|(aiei*iS!«)i*i^?i®I*i§iieio{iora^

» "

"Pre F Act to the Third EcitioN*

TttAl* favourable reception of this
Work, which has occafioned the pre^
icnt Edition of it, fo foon after two formet
•editions, is filch a proof that if has been of
fomc ufe to the public> as aitiply rewards
Ime for the attention and labour which I have
•beftowed upon it. Ih revifing it on the pre-
fent ocCafion> I have been anxious about im«
proving it as far as poflible. Several addi^*
tional fktfts and obfervations have been in*
•ferted in different places, particularly in the
•firft Effay and the Poftfcript to it, — Thit
part of the fecond Se<aion, Chap. II. which
treats of the Scotch eftablifhment^ has been
new Compofed, and carefully accommoda^
ted to the more accurate information con*^
earning it. With which I have been favour-
ed. — The 15th and i6th Tables in the Ap^
pendix are likewife additions^ which I have

b taken

xviii Preface Jo the

taken this opportunity to make to this Trea-
tife {a). The lattercf thefe Tables giv«$ the
▼alues of annuities on the longefi of two lires^
according to the mean probabilities of life^
between London and the Country ; and tho^
thefe are values which every one may» witb*
out difficulty, calculate for himfelfl from
the values given in Table VII. oi joint lives>
yet I have chofen to fave thofc who ufe this
work that trouble^ and to lay before them in
one view, the values of annuities on lives in
all cafes of two lives. The occafions for
finding the values of annuities on tbr€e lives^
are much lefs frequent; and, therefere> 1
have thought no more neceiTary in this iii-
ilance, than to recite at the end of the jlp^
pendix the rules by which they may, with
eafe and tolerable exadtnefs, be determined.*
The Supplement is an addition which
was made to the Jecof id edition.— The obfer-
vations in it on the prefent ftate of our po- .
pulation I have enlarged and extended by a
few notes 5 and, particularly, the Fojlfiripf
beginning in page 379. — ^This is a very feri^
ous ai>d important fubjedt. If, indeed, there
lias been that diminution of our people which

' {a) The three firft TaUes at the end o^ the Sy^pkmmt
have bccA alfo now firft ioferced in this work*

the

T HI It D £ O I T I 6 N. %iX

likt evi^race I have produced feems to prove>
it muft alarm every one who wiihes well to
his country^ and it ought to engage the im«*
mediate and vigorous attention of govern^
ment> A well-known writer, Mr* Ar.*
THUR Young, and fome other ingenious
perfonsj differ from me on this point ; and
I wiih I could be convinced by their argu*
ment8« But hitherto all my enquiries have
ferved only to confirm me in my firfl: con«-
viiftion. Several great manufaduring towns
have, I know, incr eafed j but thefe are no-*
thing to the whole kingdom j and even by
theh* increafey our population may, on the
whole, have loft more than it has gained»-p-
In truth ; k would have been ilrange if. our
numbers had not been declining ; for I can
fi:arcely think of any great caufe of depopu*
lation, which has not for the laft 80 years
been operating among us« I think myfelf, ,
^owever^ obliged to Mr. Toung for his re-
marks. The anfwer which I would give to
the chief of them may be learnt from th?
notes in page 183, and 375 {a).

The laft pages of the Supplement have
been occaiioned by accounts which I Veceiv*

{a) S«e likewife the fecond edition of the App§al u fhi
PuUU on tbi Subji^ oftht Natieml D^ page 86, &c

XX Prefaced t&e'

cd while diis edition was in the prefs, an4[
which came too late to be inferted in their
proper places.

The prodigious traffic now carried on iti
Life-annuities, and the rage for forming and
encouraging Annuity Schemes, which has fdr
fome time been fpreading through the king'-
dom, has rendered the information which I
have meant to convey in the following work
particularly necefTary^ And I have had the
pleafure to obferve that it has been attended
to. Several of the Annuity Societies in
London have been difTolved; and there is
reafon to hope> that thofe which ftill rtf-
main will not be able much longer to fup-
port themfelves on their prefent plans, in
oppofition to the evidence of demonflradon,
and the calls of juftice and humanity.— r-
Thefe BuWes^ however, are of little con-
. iequence» compared with that grand
NATIONAL EVIL, whlch is the fubjediof
the fccond chapter of this treatife. This is
an evil on which J could not imagine,
that any fuch efforts as mine would make
any great impreflion. Perhaps, indeed,
the united efforts of all the independent
j>art pf the kingdom would npw be too

.... . . wesik

ThirdEdition. , iad

weak to fave us from the diilrels with ^hich
\t threatens us^

ft

Much ha^ been faid for fome time of a
plan mentioned in Parliament, at the
end of the laft feflion, for paying off the
Nationai, Debt, This raifed fome ex-
pectations; and, I will beg leave here to
give a brief account of it.

After providing for all the current fcr-
vicesj there -remains this year a faving or
overplus of 1,200,000/. With this fum, an4
a profit of 1 50,000 /• from a Lottery con-
fifting of 60,000 tickets, (by a fcheme fimi-
lar to that defcribed in the pote, page 159,'
of the following work) a million and (l
HA*LF of the 3 per cent, annuities, purchafed
at -90, will be paid off (^?).-t-? When this was
propofed to the Houfe of Commons, it was
at the fame time declared^ that it would be

(«) This fcheme, applied to the purchafe of the Long^
Annuity inftead of the % per cents, would have gained con?>
liderably more for the public ; and at the fame time
given equal profit to the flock- holders. The reafon of
this is, that the market price pf the long annuity has
for many years been conftantly 5 or 6 per cent, below its
true value, compared with the price of the 3 per cents. ;
io far, it feems, do the gopd people in the Alley look be-
yond 88 years, the prefent term for which this annuity
^s payable. •

> 3 thtf

xxii Vtitf ACE to tie

the COMMENCEMENT QF A PLAN FOlt
FAYING OFF THE NATIONAL DEBT; fof^

if no extraordinary fervices fhould call for
any other application of the public furplufies^
the fame payment increafed by the intereft
of former payments^ is intended to be inadei
every year while the peace lafts : And thus,
reckoning compound intereft at 3 per cent.
SEVENTEEN MILLIONS wiU be paid off du«
rin§ a peace of ten years.

On this plan I will take the liberty, with
all the deference which becomes me to the
fiation, abilities^ and character of the propo-
fer of it, to offer the following remarks.

* I ft. It implies, that there is to be a hot^
tery every year during the whole continuance
of peace.— Formerly, lotteries were expedi-
ents for procuring money on more advanta^
geous terms, to which government had re-
courfe, when prefTed by the ncceffities of
war. They are now, it feems, to be efta-
bliihed as permanent refources never to be
given up or fufpended. — This muft ihock
every perfon who is^ duly acquainted with
the mifchicf occafiohed by lotteries, parti-
cularly among the lower claiTe^ of people.
The rage for gaming threatens the ruin of all

. * ^ - that

Third Edition. xxiii

tbftt is vif tabus and manly among uis. It is
increaiing faft^ and waqts not to be fotlered
by government.

adly> The farplns of the prefent year is
ia^part the. efie^ of foipe extraordinary fav-
logs in the laft year^ which cannot be ex*
pe^ed another year: And^ I believe, that
tfaofe who are beft acquainted with this fub-»
Jed, mud be ienfible that th^e is no fufli--
cient reafon to expetS^ while the augmenta--
tion of the navy is continued, a conflant
Jurflus of fo much as a million per ann.
l mean this on the fuppoAtion, that the pro*
duce of the SinJking Fund will continue what
it is taken for this year, and what it has been
the laft three years, or 2,600,000/. But this
is certainly more than can be depended on*
The difHcuUies of the Eajl India Company i
the ftagnation of credit which has lately
diftreiTed the public, and many other caufes,
may poiiibly occafion Difidencies. Should
there, however, be even an increafe^ it will
be owing, I am afraid, to a very bad caufe ;
I mean, an increase of our importations pro^
ceeding from luxury, and turning the balance
of trade againfl: us ; and, confequcntly, drain*
ing the kingdom of itsj^rr/^, and leaving it

b 4 more

X9dy Preface to the

more and more to the precarious aiid dan* '

gerous fupport of paper-money. But, '

3dly, Let thtfurplus of the public reveuuQ

prove what it will, there is too mudi proba*

bility that, even during the continuance ol*

peace, fome emergencies or other will be

often furnifliing reafbns or pretences for cm-»

ploying it in other, ways than the payment

of the public debts. This has been the cafe

hitherto; and from the year 1730 to the

prefent time, it has never happened, thit wo'

have gone on above three or four years to-?

gether employing furpluffes in diicharging

debts. Though in profound peace there

have been calls for a different application of

them j nor can I imagine what reafon there

is for believing, that our circurrjftances are

fo much changed for the better, that there

will arife no fuch calk for ten years to come,

fhould the peace laft fo long. But,

4thly, The moft capital defcd in this plan
is, that its operation is to ceafe as foon as a
war begins. That is \ it 'is to ceafe at the
very tirne when it would operate to moft ad-r
vantage, and when the greateft benefit might
be derived frpm it. See this demonftrated
in page 158 of this Treatifej and in p. 17
of my Appeal to the P:ubiic on the SubjeSt of
fbe National Debt, Is

Third Edition. xxy

* 1b it then any wonder^ that fuch a plan haa
had no eSc€X on public credit ? — Does it meafi
anymore than that the furplufTes of the revenue
fliall be applied to the difcharge of our debt6»
when there are no other ufes for them ? — And
was there ever a time when this was not
doiic ? I*^ not this the very plan we have been'
purTuing thefe 40 years, and to which we
owe ouf prefent incumbrances ? — Certain it
is, that nothing but a plan that (hall go on
operating uniformly in war as well as in
peace, or the eflabliniment of a permanent
fund that fhall never be diverted ; that is, in
other words, a return to the fchcme adopted
by the legiflature in 17 16 5 and which even
now ftands eftablifhed by law, but which,
through the unpardonable mifcondu6i of men
in power, has been defeated of its good
efFefts : Nothing, I fay, but this can do U9
any effcntial fervice; or^ in our prefent cir-»
cumftances, be much more than trifling with
the difficulties and dangers of the public.*-^
Eftablifh fuch a fund*— Confign it to a par-?
ticular commiffion, afting under penalties,
in fuch a manner as (hall take it out of the
hands of the Trea/ury, and form a check
even on the Hou/e of Commons ixklf. — Sup-

P^7

XK9i Preface ta tbf

fly frodi time to time all deficieocies jiift ar
if no fuch fund ejciftcd j and, by thefe and
other meafures, convince the kingdom that
ibmething effedual is meant, and that the
public debts are indeed in the way to be ex*
lU}gttiihed.-~LET this be pone j and we
i^y foon fee a new ftate of things ; public
credit may revive; and the kingdom enjoy at
leaft a chance for being preferved.-*--By the
confidence which fuch a meafure would give
in government fecurity ; but, more eipedal*
ly, by the increafing fums which would be
thrown annually into the public markets,
and returned to the public creditors, the 3
per cents, would be foon raifed to par, and
in fome time probably far above par. It
is well known, what an efFedk borrowing
every year has in (inking the funds. Paying
every year would certainly have an equal
contrary effed. It would, to ufe the lan-»
guage of a very able writer on this fubjed:
{a), caufe money to regorge in the hands of
the lenders ; and, with the help of prudent
management, might be productive of confe«*
quences the mod advantageous.

In the. interval of peace between the two
laft wars, the 3 per cents, were at 105. Let

(a) Sir James Stiuart^ Bart, in bit Enquiry int0 th§

Principles ofPMcal OeHnemy.

US

Thikd Edition. xxvii

)M foppofe that> in the circumftances I have
mehtioned,. they would be raifed to* no.
Particular advantages might be derived from
h«)ce» which I will endeavour to point out
diitindly^ becaufe^ I think, they will flicw
in a ftriking light, how much might bd
done towards the extindion of bur debts in
a ihort courfe of years, were vigorbus and
STEADY meafures entered into.

At the period I have fuppofed, inftead of
a reduction of interejiy which would only re-
tard the extinftion of the public debts {a)^ the
proper meafure would be a redudtioa of the
capital^ attended with an advancement of
intereft, by fuch a meafure as the {b) fol-
lowing.

The 3 p€r cents being at no, and, con-
iequently, an immediate lofs of i o A arifing
to the proprietors from every i oo /• paid oiF,
in order to prevent this lofs, they would
probably confent to a deduSion from their
capital of double this fum, provided wha(
remained was made irredeemable for fifteen
years, and the fame intercft continued — For,

{a) See this Treatife, page 139, &c.

(i) Since the above was written, I have Found that a
iheafure, in feme refpeds fimilar to this, has been pro-
pofed by Sir James Steuart. Principlti of PMUcal ()€€$•
mmji Vol. II. page 480.

3 ift.

VKEFACi to tit

and not on any prejent cradkors j and, conw
fcqncntly^ the fame difpofition that has
formed and promoted the bubbles which
have done fo much tniichief in this kin^
dom» wouldy in this otfi;^ be made to ope^
rate to its advantage^

I have^ therefore^ certainly kept withki
hounds^ when I hare reckoned that a re>»
dudion of'2o/. percent, in the capital of
, the 3 per cents. , might be madcj in the cir*
camftances 1 have mentioned.— —-^Let thea
fuch a reduction be fuppofed to be ^applied
to Jixty millions of the 3 per cents. This
• will Ic^^ve much more than enough free for
the operations of the fund; and by fiich
management as that, which^ in 174.9, re-
duced 57 millions from an intereft of 4 per
€eUt. to an intereft of 3 per cent, there is no
reaibn to doi^bt but it might be accompli(h«.
cd in one year, or at moft in two or three
> years ; and the confequence would be, that
ft iCapital of iixty millions would be reduced
to 48 millions ; or, that twelve millions o£
debt wo^d bje cancelled without expence or
difficulty.

But this is not the only advantage
wSiich would arife from fuch a meafure*-*-*

At

TttiRi) Edition. xxn

At tks end of the term I have mtn^doacdp
48 mflUons would be rediemabk debts, bear«
ing 3I per €ent. intereiL Thefe would fidl
aweii ahore far ; and zjecond reduftlon, on
condition of inedeemablenefs for z Jborter
ttrm^ might be applied to foch a part of
^m as it might not be neceflaiy to leave free}
and thitt, by the fame means with the foro-
goings feveral millions more might be attnl-
hilat^«'— At the fame time the fund) which
Ikad hitherto been employed in discharging
redeem^Me 3 per cents ^ might be applied to
the difcbarge elf debts bearing 3^ per cent.
intereft, and therelbre would^ as protedin
page 138, be accelerated in its operation.
And at the end of thtfeeond term» it might
be applied to debts bearing a ftill higher in*
tereft, and therefore would be flill more ac--
celeratcd.— This fecms to go to the very
limit of poffibility on this fubjed.— -Money
in a fund> never diverted, is improved
at compound intereft i and, this being the
very beft improvement of money poffible,
there can be no method of difchargtng debts
fo expeditious. But by the fcheme now ex*
plained^ the operations of compound

fNTEREST ITSELF WOULD Bl AIDED* It

would

, would be eafy to Jhew» that; in 40 ^^adj lAd

-without the aid of Lotteries^ a hi^niired

MILLIONS of the 3 per cents* might in this

: way be difcharged; with a prefedt aimual

furplus of {a) no more than. goOsCQoJ. to be

increafed in the year 1781 by aooyooo,/. (A)

; which the public will gain by the redusdUiOn

of the confolidated 4 per cents*, to 3 per cints^

And this^ without all doubts is near twice

.a3 q[>uch as can be done in theiacne time

-with the idssi^ furplus y by any othfr ^aitabfe

9ieans*— With a prefent .2tViXiMs\ furplus of a

millfonf no more th?in tiJ^nty-Jive milX\(^% qf

the 3 per ^/7/j«.woi)ld. be converted initp lifft*

{a) About twenty millions would be difcharged
Without ^any dtfburfement of money ; and the remainder
would be difcharged by the accumulation of the yjm^^
applied, for the firft 25 years, to the payment of debts
bearing 3 per cent, intereft, and afterwards to debts
bearing higher interefls.

The management above propofed might be applied to
the propofal in page 156, and would very much 'improve
it. — That propofal requires a prefent furplus of a million
and a half ])^ annum \ and could fuch a furplus be gain-
.^d, Qur deliverance would be rendered much more pro-
bable and complete ; but that being more than can \afi
obtained without retrenchments and favixigs, whicfi,
however pradicable, are not to be expedked^ I haUe
been induced to enquire what might be doue with
fmaller furpluffcs.

(i) In 1782 there will be another faving gained, from
the redu£Uon of four millions and a haljy 2iP*^ ^^^' ^^'
Buities, 1758, to an intereft of 3 per cent,

7 annul-

T rf i R b E t» 1 1 1 6 N. xxxlli

tfliritutks^ fuppofing the proprietors, one
Wilb another, to aeccpt, in lieu of cvSry
l<wA ftock, 7/. per annv for life. And
ffee whole incumbrance' on ' the public occa-
fibned by foch annuities, -would not be en«»
tirety' rebiwed in lef$ tbaii ftventyy or pcr-*>
iMjftb leighty yearsi

Were a furplus of a million per arm. em*
^oyed :in: converting the 3 per cents, into
long annuities^ a hundred millions might in-
deed be difcharged, by locking it up for a
term di years, and offering the proprietors
4/. per ann. for that term, in lieu of evejry
1 00 A ftock. But it would be necefliiry to
make the term much longer thzn forty years.
He that will conlider . the low price of the
long annuity now at market, may fatisfy
himfelf^ that no terin . ihorter than ^(;^ or
feventy years would he accepted $ and the
fame furplus^ locked up for feyerity years,
would, in the way I. hare propofed, dif«
charge three hundred miii;«ions«
' I mail repeat here what cannot be too
;much inculcated, that a war would have no
other eftedt on fiich a fcheme than to aid it,
iThc operations of the fund, would be quick-
> c ened

-rr^

^xiv Preface «^ tie

ef>e4 in tb« raaniMr Qxplainod iir jiig*
1^7^ &<;. And, fiipp^ag no divorfioof of k
c}uripg the exigences of war, fuch a denftoor
UfaHon would be given to the pubUc» thafe
an ttnalt^mblfi pUa WW At hft tA«bU(lMd»
as. could. Aot 1^1 to produce, the hapfMA
eiFedts; and to enable govenim«st« wtiMt
peace came, to carrje into execution fach
meafures as I hjsive propofed to the greajbdE^
advantage*

' The lofi of the xt^YOtiJvrplus^ in a tino
of war> is a kfs that muft be Submitted to#
whatever plan is. adopted > nor would k, ia
that which I have propofed, be produAivc
of any additional bnirdcnB or difficidtkn*
«N^Ia' war it would, be Qecrflfary to bbrmw
ijbvecai ndlUonrS annually ; and, at fuck^ time^
the ne^effity) of bort owing am mlUon extras
wdinaxy could xx)t make any great difie^
reocQ: And^ as this would be, done to conr
V£y ^ convidjpn. with .which the very power
of borrowing was conaeded, and to^ prejfervc
zftmd on which the very being of dbe ilate
depended, none, but the bed: confequenctas
could arifb ftout it. The. public burdens
wionld be even. k/s. increa&d by a war^ in
I \j' . con-

T H 1 A » • •£-•» I * I O N. -XtXif

€oBf«qe<nk« tt Wiitg a tkiiilidn fif ^ttntttk

itt^^ .it» ^MiMiiftC^ thA9 Withdrawn

fr6m^die fuppiifcst For>-letQ8 iUppoTe^je
MhSSkMI heo^iy .to b6 tk)rK>wcd evttf
jrd^ i{6 iAefirft^ tho expenced of Wift ^$v#
jiraDS0»3< «<)iy 4>f ^ich iwoold bAV« btcA
1»fakiMd» had not th« mUlioli Jhrf/uj b«en
kckoA ttjK<***'^-^tfpf)idfd farther, that th«
&htme, by ktse^dg up public credit^ and
throwing montiy every year into the hatMift
of Iieiidef », enabks govertiMcnl to borrow at
1 1, 'per £€Ht. left intereft than would bt
otherwife #equired« or at 4 iniWdd df 5 pet
eent.-^In thefe circuiAitaMes, there would

■

arife a prefect faVing to ihe kingdom of
10,000/. /^r ann.i for the intereft of^;r
milfions at 4 /^ r^/tf. is lOiOoo/.Jefs than
Ac intereft <}i Jhe miliiom W 5 per cent, {a)^

And

» •

(tf) There would, indeed, be an increafc of capital \
iM iMi .^^ bave biihejto never regarded, when it h99
not been attended with an tncreafe of intereji. In the
^dieivt . taCr, howeter, it would not be nec«ffary, that
.4^ increase of caBkal iboukl make any additigji to the
publip. burdens, ^or,

(ft, The icbende might foon be applied to (Be capltaf^
mid would c^SMel it falter than the capjtal of ^pir j^itU^
•n.aoQE^Mi^.of the higher intereft it bore^^ ';

2dlyy The {trice of it would, when pcatce came, rife
fm above /ar I and, therefore, it might cafily be reducea

c 2 from

And fiich a.faving, rep^a(G4 wcryiji^ of-.#
w^r» would be an o)>jfd of (otj^ V^p^tfmfifi
to the kiQg4om,^^IiKleed, there mdy^lff^j)^
poiCbility of Gonc^iviqg whs^ ^mp^^^itaot
c^ed^ in thi$ way^ the^ ed^blifl^c&cvt ^ fucb
a fcheiBe might produCiiKb Pi>^!M^ its pro«
grefs in difchvging pur debte^ and; bqfarje it
could give, any relief by the-.annihUatipn of
tax.es, it might /ave ;the.luog(lom, by^ pre*
ferving it frpm difi}ci4tie8 .wi^ich jvoi^^^^av^
funk it, ; And every one mnft he ieiiiible of
this, who h^sconiidCfred wjiat danger there
is that a war, ihould it becQD>e .iinavoidabi5
before our debts, are .pji^^into any certain
method of redf^mption, .will either, entiwjjf
overwhelm public credit, or fp much weaken
it, as tQ produce an imppffib^lity of bprrow-f
ing* .except on very exorbitant ipter?ft, and.
confequently, of finding taxes fufficicntly
produftive to pay fuch intereft.-— The gene--

■ I

from) fix to five millions by the management I h«\re tx^ '
plained. - '

' 3clly, There arc even mcthod$'by which JLr milHMs
Itiight be borrowed at 4 per cent, and the capital fixed;
without ipconyenience oj diftculty^ ifd five millions,^ t
Thofe who do not chufe to give me credit for this^ may.
If they pleafi^, think it a miftake. The fall explanattoil
of , it would lead to an account of the' beft method of
toiitradling debts, for which I havt here no room.

Tut nth EniTid'-K. xarai

nllt^rthenfMiitliQW!: &t'that- the nation it

oraf loaded ; ^and thaftitdd^bts will adverts

pftifl^ :Tbisi;ki3ep» n^^rftinds near i$ /^i^

riM.ilbwcr tbaA tb^.w^re in th^ I9& f^^%

16 the Mii:waf iiic^ np^irclicqfion* vUlin*

^0cafe(r.«nd).|irotli»c«:: giVAt diPgtffi. ; 3ut

0)ould it be then icen^ that a plae ^Qf r^

deeming our debts, the moft efficacious that

pod^QiKt^iiretftalki^^ WAsgoiBf^iCliSr <!|id,

4».n)ftft(|!Lienfie : of otteln^ .'guarded in Ibipf

^bckim^nner. as; IJias^rbilitiBd, icdar/^not, or

^tmU-notfU^^y, bccrcawked ; in tbefe CircunH

tfbmce8y:all d2^»gcb vf^^mH be fi) ffu: Jeif^n^dii

•thaL it. might be jira^icable to find^^rtpw taxe$

Vrliich^ would fuppWt/ th^, e^peoC<5 &f war

diiifing thc:operatiobs{o£ll\e'fchcm§.T-lC any
oneibielieves^tbe cortti^y,, let h^m, 4n God'?

inamei thintc what: 9 coftdltiop w>^ ar? ip-rr
IJiopfi onr -circumftanfre^ ;a^. not fp defpe-^
;rate.r-^ — ^Many' (aviqgs might certainly be
^ad^, without partiguljar difficultyj, in thf
coll?6lion and expenditure of the revenue. —
Ji coniicjerabl? ahnu^l incopxe iniglu.be de^
.'rived ftom taxes ppon Aorjes, Jd^s^ iivery^
fenxanUt and celibacy ; from an increafe of thp
\%zx xx^t^n eoackes and plate i and froin atajc

<tti oil legacies and AicceAodt m tithitkn
The laft tax '^oald b*^ ontj^ obl%ingLtlnA
Who lihd enjoyed thiptonGdAntd i&eikalf
during )^e, td cbimilKiM^tbiwiwdfiiliiiipport
at 6te^i And -ait the^^ cither tttw vrouM
htecffasffy do gooid i&">viibm^yet mzyibaf

• — I ' • ■• t . ■. .": J ,- . • • •• I,

' Bist^I'am got fyff btyomd tic limits T pre^
^ibed^byfetf whcsi I>begun tfau Pftfiucc^M*
As die lUKtional d&bt is a fiibjed: oa^eaktUjr
TMtrtAkig^a) thtki$ aatioii^ I could n6t\ai^
ioW myfdf to omit any thiog that appearafl
to me of conlcqiionce' upoa; it ; and dbefilea^
der of tkb Tre^tile will on this accoimt^I
tiopey cx^Ofe m^, if^ I have detained ihia
here too 'long and too im properly .-**4n fts-
vieiHng what I have-> written, I am indeed
almoft difpdfed to congratulate myfe}f on
having pointed out a method of difchai^ging
the public debts in a ihort period of .yeai%

(a) Mr. Gordon tells us» that the great and g09d
Mr. Trencmard had two ' things imicb at h^ari,
namely, keeping England qIqm of foreign Imoik, aD4
paying off the public debts. He thought that one of
thefe depended on the other, and <bat iiifgU ^rndtting
fjf ^he Siati depgndei on the bttttr, Mr.. GoJUJdO^ add^,
that he believed no one who thought at all, could' think
'Mr. Trencharp miftaken. Preface to Cato's Letters.

with

r

TsiKB EsiTioM. zxxix

with ^furpba now in our poiTeffion^ and the
INVIOLABLE appropriation of which will
never be felt^ except in efFeds tlie moft fa-
lutary and beneficial ,-^But I fall back into
difiidence. Much has been before faid on
^8 fobjed by writers of more confequence
to no purpoiie.; and we fliaU purfue the
path we are in^ till the edge of the pre*
<;ipice towards which we are lulvanciog
awakens us, and ruta beconott cerlain. and
pnavoidable.— The diftrefs occafioned by the
ihock lately given to the bubble of papcr-
credit, is, lam afraid, a prelude to unfpeal^-
ably greater calamities, and a warning to
prepare for them.

ERRATA.

r

V

E H R' A T JU

Page 41. hne 6. y^r marriage in feven fails of leaving
chililnen that furvirc their parents, read one in feven
of all Who die widowers leave no children.

Page 79* Ufu 14. fir exceed confiderably the numbef of
marriages, read exceed confiderably balf the numbef
of marriages* ^

••• ♦

Page 316. column 3. of the firft Table^ Unei from the

bottom, yir .0199, r^tfi .0899. * *

^

i >

l*tfWW8

C H A p. I.

^utfiions relating to Schemes for grant-
ing Reveriionary Annuities, and the
Values of AJfurances on Lives,

Qjp £ S T I O N I.

FjJI^M jClJI ^^^ ^^ married men enter into a
V ** A W ^' ^i^ty ^^^ fecuring annuities to
^ ^*^ their widows. What fum of

kl^3K%jrf " money, in a finglc prefcnt pay^
^* rnent^ ought every member to contribute,
^* in order to entitle his widow to an an-»
nuity of 30 /. per ann. for her life, eftimat«
ing intircft at 4 per cent f"

Answsr.

It is evident, that the value of fuch an ex*
pedation is different, according to the diffe«
rent ages of the purchaiers, and the propor*
tion of the age of the wife to tht^t at the
huiband. Let us then fuppofe, that every
perfon in fuch a fociety is of the fame age
with his wife, and that one with apother idl
the members when they enter may be reck-

B on«4

• p

2 « " ^iMjima^fioMMimg

oned 40 years qfSge, as many, enteripg abdye
this age as below it. It has been demonArat-*
cd by Mr, De Moivre and Mr. Simp/on^ that
^V the value of an annuity on the joint con^
•* tinuance of any two liwB, fiibtraded from
'^ the value of an annuity on the life in ex-
** pedtation," gives the true |)refent value of
an annuity on what may happen to remaia^f
the ktter^c^ the Vf^ny tivee <«ftfrr fkc otker.

In the prefent cafe^ the val ue of ao annuity
to ht enjoyed during the ^int continuance of
two lives, each {a) 40, [hi) is 9.826, accord--

ing

(0} See TubleViL Appendix.

\h^ The Tatars of j'^mi^tvciantl rt^erfiosi, ai deduced

.<roai tbe 9$ts/kut obfervatione^ we tt6t givea in any part

of lhi€ wofk from Mr. i>« Moiuri%.^^t%nti hn tntatiie^n

sCn Wities on live^: For thef<p' rules .are approximations,

'\irhieh give rt/uUs fo far fr^in (he truth, as to be^ not

oiily'ifffeMrs,-4Mi^<i«ngef4ui«* 9fi «he fecond cflay in the

- jflWWOtoCj^l^ aa«Wbl?r -aqwmt-pf thi$ wU be givcfi»
and alfo ot the method in whi^. tb^& values have been
calculated. * . « ^

Mr. Di Moivri'h2S calculated the values of ^ngli liveSy
on the fuppofition of ao ^ja$af Acnfment of life thro* all its
ftages till the age of %6, wHicIt h^ coniidered as the ut-
owft^probaMe^xteixt of lib* Thm ; 4«t there be 56 per-
foos alive .at 30 years of age. Tt is' iuppofed that one will

'die drerjr^eir w!, in 56 ^etrs, they -wHl be all deab.

' The >fifl^t '«(ll'b^ppcfiito^jat4^, »ui4( yesrs. To 36
It s^ >P ^^ i^cH »f^ io^f>n{for ^aU />tber a^. The
number of years which a^givop life w^anKs of 86^ he calls

•-the iof^pMent df *atiife.- Fifty-fvc, therefore, is Che

. TUs*hypptHofis.€^i(^ veiy iBuph ihp hjbour of cidi:sKU*
ting the vzlucs, of lives ;, and.it js fo conformable to Ilr*
Tfafky*s table ofobf^rvitidflsy'that (here is little or ho rea«

j ^ • fon

« *

»» m^ 10

iug tp t^s prpbs^biUties. of lifer |q tl>e TahU of.
Obf«rv;)(^Dfi fo,rm«d by Dc. ffa^Jley, frpiv tlji; .
hUl$ of mortality of Brej[lav in Silifin, - TW
value of « iioglc tiff 40 yeafs of ag$, (u ^^Y5')
bj Mr. />f Moivrt, agre«cU?iy to the faqae Ta**
l>le, is 13.20 (a); ai)4 the former fijbtra^^
frcrm tjbe latter, le^vc^ 3-37» o*^ th« tr^« nn«)-
1^ ^ ye^n porciMfe, yvhicl? ougb( p be
paid for any given gqiiwity, to b? ?ry9y«4 l?y a

ibft for diftinguiOiine between the values of lives as de-
dMGtd from ttiis Table, and the fame values deduced from

lo prder tp ^yoid putting the reader tp trQubIe» I b?vf
givjeo |his tabic at the end of this lyorV* And I jiave alfo
given two other tables which I have formed from the b|JI»
of morralit^ at N0rthapfpton ami Norwick. Th^fe Jaft
t^blea Jiofwer more nearly to Mr* Di Maivri^ hypothclis
than even Dr. HaUef^ table ; and the difFerrnce between
^e values oifingk^nA joint lives by the bypothejis^ and the
{^mit values coipputed firiAly from the tables^ it geae-t
za)Iy \%f^ in tbefe rabies than in Dr. /b/fry's, as ^iV^ be
Piewn in the laft fiiTay. Wheq, therefore, in the courfe
of this wgrk the values of Jingit and joinf lives are men-
tioned, as given agreeably to Dr. HalU/u table, it muft be
u^derftoodt that £ey are taken frotp Tables V{. an4 V^«
in th^ Appendi;(t ^ f}^^^ ^ A''^^ zfpefim^nt only fp tb?
hypothejls \ and that for this reafon, they are in reafitv ftill
moreconfermabk to the Northampton and Norwich tames.

The injiabitant^ of Londpn, as is well knowOf not IJK-
iog fplomg as the reft of ipankind, l))^ values ofjinzk^ni^
pint lives there, are coniiderably lefs than thofe ju^ men-*
tioned. And^ therefore, whenever I have had Lmdon
lives in view, I have given particular notice of ^t, and
taken their values from Mr. Simpfon^ who has calculat-
ed them with much accuracy from the London tables of
obfervation. See Tables X. and XL

(a) See Table VI. Appendix.

B 2 perfon

4 ^ifiions edncerning

perfon 40 years of age, provided he furvives
another perfon of the fame age, intereft being
reckoned at 4/>^r cent, per annum. The an*
riuity> therefore, propofed m this- Que ft ion
being 30 /• the prefent value of it is 30 mul-
tiplied by 3.37, or loi /. 2s.

By calculating from Mr. Simpfon^^ Tables
fajf formed from the bills of mortality oi
London, this value comes out 102/.

The difference in the value of the reverfion
will be inconfiderable, whether the common
age is taken a few years more or lefs than 40»
Thus married men of 30 ought not, accord-
ing to Dn Halley^s Table, to give two-fifths
of a year's purcnafe more, for any given re-
verfionary annuity for their wives, than mar-
ifff&mtii of 50, provided they are of the fame
agin with their wives ; and one quarter raore»
sicJcWWKng to Mr. Simpfon*s Table. If the
Wives are younger (as is generally the cafe)'
there wiliiodeed be a coniiderable difference ;
forthe^vafaie now determined would be 120 /•
according to the Brejlaw Obfervations, fup-
ppfing the two lives to be 40 and 33* or
that wives are one with another feven years
younger than their hufbands ; and 1 1 8 A 10 s.
accordii^ to the London Obfervations.

/«^ Sec Tabic X. and XI. Appendix*

> . >

Qjtx ft s*

Reverfionary Annmtiesitxx:. 5

QjJ E S T I O N II.

^' Suppofing fuch a focietv as that idefcrib-
*^ cd in the preceding Queition, to be lilnit-
'' ted to a certain number of members^ an((
f' conftantly kept up to that number, by the
*^ admiflion of new members as old ones are
^' loil, in confequence of their own deaths*
*J! and the deaths of their wives : What is the
^/ nun!lber of annuitants which, in fome time
^* after its efiablifhment, will come to be
•^ conftantly upon it ?

A N S W£ It,

Since every marriage produces either a
widow or widower ; and lince 'all marriages
taken together would produce as many wi-
dows as widowers, were every man and his
wife of the fame age, and the chance equal
which (hall die iirit ; it is evident^ that the
number of widows that have ever exifted in
thjt world, would, in this cafe, be equal to,
baif the number of marriages. And what
would take place in the world, muft alfo, on
the fame fuppofitions, take place in this fo-

ciety. ^^In other words 1 every otbtr per-

ion in fuch a fociety leaving a widow, there
muft arife from it a number of widows equal
to half its own number.— --But this doea not
determine what number, all living ac'cnomnd
the fame time, the ibciety may expeA H^ill

B 3 come

6 ^pdm):€ncerfting

come to be conftantly upon it. For if every
widow lived rid more tbui a year, the fociety
Would never have more aiinuitants upon it,
than caaie on in a year. Aild on the con-
trary. If none ever tlied, the number of an-*
oujtahts would go on increaiing for ever.—
^is^ therefore, nccelfary, in order to anfwer
ttie prcfent enquirjf, to determine bow long
\h^(^r0ti(af ot/urvivorjhip between ^x(ov\%
ol^.^^V^ k^s will bp, compared with the du-,
rattan Q^. marriage. . And the truth is, that,
iuppofirig the* probabilities of life to decreafp
uniformly f^aj, the former rs equal to the
latter ; and confequently, that the numbdt
of /urvivors, or (which is 'the fame fuppo-
iing no fe^pnd marriages) of widows and.W-*
^(?w^ia^vc together^ which wJll^afifc from
any gi^cn^ iet of fucli rharri^ges conftantly
keptj ug,^ will be eqaal to the whble nufjj*^

}Pifjmf^^^^i^^.? pr, half hfxhcrri (tjie nuin-
Rec of:wi^ws in pfrtiCular) equal to half

' /f^iT'i^^ ^'^ fuppofing "that out of any given number
ilfv{j'««rfyi^e, Che fame finiiibcf wiH die cf cry year ^11
ax Xi^ Jkluf. See tlie {>^eceAng note. That cft» this )stf^
l^othffiii,' ttif) iltivation of funrivori^iip is equal t« \\h A}kf
ration of marriage, when the ages are equal \ or, in othe^
wbi^dl,' ihflt the exptQdlioh df tw6 joint lives, the ages
]Jtrffig cijw,' is the Iknie Wreh the txpfffaihm of'fiirvivor-'
ftip»d|iay.ic;}avnt fvom the !i Mr and 20th.prqb)ems.of

tionw jt, together vrith a particular explanation oftnis
^jfcd, W/%trfctiAitfbrThe^^ttmtig of the fixh Effay,
lbnMhidil1^ifft*b«g. ilte saai^er t6 ixtcxL, if he is at toy
\\i!$ nJCiOfkt .tb^ Cull mf aoing of what is here faid,

^ ■• tho

.*(

Reverjonary Annuities, &c. 7

the number of marriages.— Now, it appears
that the decrqafe in the probabilities of life,
}s in fadt nearly uniform. According to the
Brejlaw, the Northampton and Norwich Ta-
bles of Obferva^on, almoft the fame num-
bers' die every J '"-' — -- -'' — *~

77 f^J' After

bers die every yeat from 20 years of age to
77 f^J' After tnis, indeed, fewer die, and
the rate of decreafe in the prpbabilities of

life is retarded. But this' deviation from the
liypotheHs is inconnderable; and its eifeft,
;n thejjrefent cafe, is to render the dui'^ition
«f furvivorfhip longer than it would pther-
wife be. S^ccovAing to th^ London Table of
Opfervatio ibers dying every year

Inegin to.gi CO years of age } and

jErqm hena le oljl age, there is a

conftant n 1 the decreafe of thp

prbbabUitii \j. U^pon the whole,

therefore, it appears in aniwcr to the pre-
Icnt Q^eiftion, that'", according to the three
'"'jormer Ta,^les qf Obferyations, "and fuppo-
'**'fihg no widows, to marry, the number
" enquired after is Jbme^hat grtater than
." half the nyniber of the foci'ej^ ; but, ac-
** cording to the London Table, .a good deal
f* greater." ' ^■

It muft be carefoUy rcatembered, that this
has bceq dcter^acd on the f^f^i^qn, -Aat

■ (a) S« Tables Ilf. IV! and'v. Appendix.
(b) The reafonor tbu difdrcsce betireen tht iMdm
and other Tables, will be-gtTen tf tbc ewA of'tbe fourth
Efflay.

B 4 huibands

8 ^efiions concerning .

hufbands and their wives are of :(fua]"ag^^
and that in this cafe it becomes an equ;»l
chance which (hall die firft. In reality nei-
ther of thefe fuppofitions is joft* Huibandl
in general are older than their wives ; andy in
equal ages, the mortality of n)ales has been
found to be greater than the mortalitj^ of fe«
males. For both thefe reafon$» it is much
more than an equal chance that the hufbaAo
will die before his wife, or that the woman
(hall bp the furvivor of a marriage^ and not
the man. This will increafe conliderably
the duration of furvivordup on the part (^
the woman, and confequentjy the number
enquired after in this Q^eflion. The mar^
riage of widows will alfo dimipj(h this qumr
ber, and the operation of thefe cau(es will
be different in different fituntions. fiut it if
by no means to be expeded (in the fituatiotk
of the focieties I have in view) that the di«»
minution from the latter cau(e will be coi^r
fiderable enough, to overbalance the opera?
tion of all the other caufes which have be^
mentioned, and reduce the number under
confideration fo low, as half the number of
Tdzxxxzgt^ fa) .

Scholium.

In London it appears, that there is a re*

tardation of the decreafe in the probabilities

. . . . • •

(a) It will bf obferved hereafter, that this obfcrvation
bai been found lo be true in faft.

5 of

Rive^^hnary Aftnutttes, Sec. 9

of life, wliich renders the duration of furvi*
vorihip between two lives of equal ages^ con-
fiderably longer than their joint continuance.
It feems worth obferving, that this is the
reafon why, though the probabilities of life»
and therefore the values of fingle and joint
HveSy are lefs in London than in other places^
yet the values of reverfions depending on fur-
Vivorihips, axe - in fome cafes greater there.
It is proper to add> that this likewife is the
reafon why, in calculating the values of Joint
lives and reverfions, the prefent value of aii
annuity payable yearly to the furvivor of two
equal lives, may coitio but equal to, or eveil
|;reater than, the'f^refent value of a like an*
nuity for the joint lives* As an annuity, du-»
ring inch furvivorfliip, will probably not be-^
come payable for (bme years, and therefore
^e money given for it wiU have time to ac-»
cumulate; it is manifeft, chat the value of it
could never be equal to the value of an ahr
nuity on the joint lives^ the payment of
whkrfa begins immediately, were not the ob-
fervation now made true.

QjU E S T I O N III.

^ Such a focicty as that defcribed in the
** precedijng Queilions being fuppofed ; in
'^ what time will the nun^ber of annuitants
'' upon it come to a maximum ?"

A N s-

JO ^ejlkns concerning

*' , .1

• »

AllSWBR. I

In :of4sr to be more <:Iear in anfweriag tlnv
Que£ion, i ^ill £rft fpppofe the fpckty to
^reljpeQd in it /roaji its firft ftfta}>U(hinenty
^ the maprried perfens of ^/£i^ s^es ip ^y town
or country 9 where the number .of pec^^Je f our
tiiiu^ conflantly th^ fame. . In this pfe^ ,^^
w^holc cpUedifve bo^y of memlv»rs will b^ «t
tbeir gres^tefl age^ at <he time of the eftaoK^^
menf of the fociety^f and the number of
Daembefs^ together ^idi the nfimiber of .wi^
dows , left every year^ vt'iXit te^ipg QHf . year
jvirth anoth^, admit of no iAf:r$iafe,or dk^u**
n,utioa.. The nij^tnber of widows in Hfe tfk>
^ether, derived fr{7iQrap^ gi^F^^ njip^bj^ coa>t
ing on 2^ ibciety '^ery year^ iwill \t\%xf^^4^^i^
tiaually^ 'till as \p^y ^ ^ff %Sy ace a^^j?^
every year ; that is^ '(nil they Qogje^ to die- p^
^ fail a^ poffible. • Bpt thicy cam^pt ^ie-of
^$ fail as poifible^ '^Ul ^ wholis «iolle(^ive
bWy of widows ^r^ at thw gf ea^(f ^. 48^-i :W#
'till there is among them the great^aua^ef
poflible of the oldefl widows ; and, therefore,
not 'till there has b^en time for an accefHon
to the oldcft widows, from the youngeil jpart
vf t?re widows that come on annually,

L?t us^'for the Take of greater precinop^
divitle the whole mecfium of wlaoivBf %at
come on every year. Into difFereht 'chub& ac-
cording to their different ages, and fuppofe
fome to be left at 56 years of age, fome at 46,

fomc

Revirfhnafj Annuities^ &c. 1 1

fohie at 36, and fottie a* 26. The tvid6w$,
conftantly in lift tbgiither, derived from thft
firft ckfs, will come to tfeeir greateft age,
0ftd to a tndxh^fn^ ift 30 years, fuppofing
^ith Mr. De Moivre^ 86 to be the utmoft
kxttnt of life. The fame will happen to the
fecOnd clafs in 46 yeard, aftd to (he third in
50 years fa}. Btit the whole body, compof-
fcd 6f thefe claflfes, \^ll not come t6 a maxi^
inum^ 'till the fame happens to the fourth or
yotittgeft clafs 5 that is, not 'till the end of
60 years. After this, the affaifs of the fociety
Will become Jfati&nt^j and the number of
annuitants upon i* of all agfes will keep aU
Way^ nearly the fame.

• • *

SiKh is the atiAver to this Queftion, fup*
pbfihg a fociety to begrn with its complete
ftunibfer of me'mb^s, cdnfifting of married
berforii of all'^ges, in the fame proportions to
ohe Another, wifh the proportions in which
rkey exift in the wbrld.--^— *-If it begins with
iti ccAnpIete number of members, but at the
lame time adthits none above a particula!r
fg6t . If, for inftance, it begins with 200
midmbers all «6dfer 50, and afterwards limit?
iffelf tothis number, and keeps rt ap by ad*
iphting icvery year, at all ages between 26
ttrid ^o, netv tnembcrs as old Ones drop off j

'X^) im the Appifidixy nt)te (A), z nule Ugiven, by wbi^h
the numbers alive at the end of any particular number of
years may be very eafily determined^

in

I a ^ue/iions concer$iut^

ID this cafe, the period neceflary to bring, ofi
i}^t maximum of annuitants will bejuftdpU'^
bled. For^ in the firft place, du whole ippl*
ledive body of members will be 60 years in^
getting to their greateft age, as may eafily
appear from what has been juft faid. Thii
annual medium of widows, therefc^e, that
will come on the fociety will increafe con*
tinually for 60 years; itbeiog evident, that
the older any fet of married men are, taken
one with another, the fafter they will leave
widows. And after this annual medium it
ihcreafed to a maximum^ 60 years more will
be neceffary to bring to a maximum the num*
ber in life together, derived from fuch ^ fixed
annual medium conftantly coming oh.' If
fuch a fociety is any number of years in gain-
ing its maximum of members, the time neT
ceiTary to bring on the maximum of annuitants
will be dill further prolonged, and will be
equal to twice 60 years with that number of
years added. — M oft of the focieties for granf^
ing annuities to widows are of this kind;
and, therefore, fuppofing them to gain their
complete number of members in ten years»
and for ever afterwards to prefcrve it, the
number of annuitants upon them will go on
increaling for 1 30 years,—It is proper, how^
ever, to be remembered, that the increafe
will be quicker at firft, and afterwards flower ;
and that, within 20 or 30 years of the epd

of

I

Reverjhnary Annuities^ (cc. i^

tt this term, it will be fo flow as fcarcely to
be fenfiblet tbough ftill real.

All who will beftow due atteption on this
iubjed: muft fee thele decifions to be j oft;
tnd i demoDftratioti of them might be givea^
in a form more ftti&ly mathematical, were
it neceflary.

QjllSTION IV.

Suppofe the members of fqch a fodety
as that defcribed in the preceding Q^efti*
** ons, to chufe m^ingannual pigments during
the continuance (^ marriage ^ in lieu of the
^^ fum which the reverfioaary annuity for
^* their widows is worth in prfftnt money :
'^ What ought thefe annual payments to be>
'^ eftimating intereft at 4 per cent V*

tt

t€
tt

Answer.

, This will be eafily determined, by finding
what annual payments, during two joint lives
of given ages, are equivalent to the value of
the reversionary annuity in prefeni money j--^
Suppofe, as in Queflion L the two joint lives
to be each 40, and the reverfionary annuity
30 /. per annum. An annual payment during
the continuance of two fuch lives is worth,
according to Dr. Halley\ Table of Obferva-
tioiis, 9.82 {a) years purchafe. The annual

(a) Sec Tabic VIL

payment

14 ^efikns cun^^rmn^

payment then ought to bq fiK:h a^ l?ei{ig R|pt«
tiplicd by 9.82, will produ((re.(4) V.jpx.*ritl4«|
prefent Takie of the aaoaity* io mit^ {i0tyit|(nt
by Queftton L Divide, tl^n /«ipi.i \kf
9.829 and the gmtimtw m I. xckj wiU l^it
the anrwsn»*Tf^TJiis i) very wm\f the siin
jiual payment of all the member^ at 99 4ven
rage, fuppofine equal numbers to offer them-*
felves for admifiion of evo'y age between 3 o
and 50, As n^uch a^ fome give lefs, pthers
ought to give more^ accpr4ing to th^ir ex-
cefs of .age. Thus, the annual payment of
H marrigjcTperfon, 30 ye^rs of age, ought tp
be/. 9.393 and of a perfbo 50 years of age

/. 11.33^ If the values of joint lives and of

the rpvprfionary annuity arje tajcen agrce^ly
to the London T^ble of Obfcrvations, the^
annual payments will be, for 30 years of age
{b)y /.10.9, — for 40, /.1 2. 5, — ^for 50, l.i^.^.

If

(a) Paxticubr notice fcpuld he tajcen of the r^ofhoi
fA notation here ufed, bepaufe jr will be carried througli
the whole pf this work.— ^ — The fig^rea on the right
hand of ths fuU^ppiot, {vgvify the depimal pfM'U pf i /«
IJbu3i />U)i. jf i3 101 and fhc jQXho/ 1/. 9/ /.40;
^nd ^j,— — r/. 9 39$ 4^ /• 9, and 39 ^undjedths .of i/. or

19:7/.: xorf. /•n«y3> is /.u, and 3^ huiidseflchA

^f il.JM L II : 6^. : 7 rf^ ^m In igeoecjil \ i/t ibotiid ^f
«e9l|fBbeffd, %^H 9 flvilin^ allowed for every unit J0
*t})elirftj)ljK:epf decia)al^, and two-pence half-penny f((K
^very yqit io the fecond place of decimals, wfH give,
nearly enough, rile value of the decimal p;ift of €V/er.]p

(b) The value of two joint lives of 30, taken from Ta-
ble XL is 9.6. This fubtrafled frgm thp valye of the
life in expedtation, or from 13.1, by Table K. givc« 3.5,

the

If either the rate of intereft is fuppo(ed
hwtx^ cr mvet aHe . i&ippo6d younger than
tb^tr biifl>ands> thur^oatl pajrments mil be
iacreftf^d. Bat thene is Jiowxa&on for point*
iftg oitf pafifekuhrly the difibrence. It may
kc etfily foDod in any cafes by the dir^Aions
Hovr gives. There b, however^ one obfer-
Talioa ^tch oogfat to be here carefotly at-
tradKi to.-^Thk method of calculation fup-
^pqfes> ^that the firft aamsal payment is fiot
to be nufede 'till the end of a year. If it 1$ t6
be made immediately^ the valae of die joint
lives will be increafed one year's purchafe ;
and, therefore, in order to find in this cafe
the annual payments required, the value in
Itfcfent money found by Queft. h moft be
divided by the value of the joint liveis in*
creafed by unity^ an4» in this way, the pxe^
ceding vadues at 4 per 4:ent. according to the
Brjsfiaw ObfervationSy vfSA be found «o be
/.8 j6^&^-'/.9. 3 5— /iio,07.~ According to •the
London Obfervations^ /.io,— /.i K2> — r/.ia.y.

I . . ...

jhe 'ttraiber of yeara puvoh^fe ^ch an onnu^tgr i^%\)f^
of 30 years of ligc, afier anoijier life of the fame a^e, is
^WOlth. This x^misifnder, midciplied by 30, ^ve8^05f.
<tbtvadue in a fiiigk pavment^^ypjpofing the- reveif^efy
MiQuity to^ be 30/. ^nd. ip$ h nAWi&i kj J9i6, '^ufi9s
/. 10.9, the value of the fame aniMxity in aonual pay^ents^
'during the Joint cootipuance of the two llVes, according
to the Lm£»irobferv«tiohs.-^By 'iim^kr operations all the
mother rahiea nhoTe^im hiYC been IbuncL

« • V •

QjJE s-

i

4€
€€
€€

€€

x6 ^^fikm coHfirning

QjJ £ 6 T I o N V.

A fociety xxmiy chtiie to make abate*
ments in theib annual pa3rment8» and to re«*
quire the remainder of the value of ^t
re?erfiouary annuity to be given^ in fine»
^' or pretiiiums at the time of admifiion. It
may, im inftance, chufe to fix the annual
{Miyments of all the members to 5 gummas.
*^ What, in this cafe, would be the premium
'* due at admiffion, the annuity beihg fttpd%
•^' pofed 30 A per annum y and intereft being
" zl /^ per cent V"

Answer.

From the whole prefent value of the an*
nuity in one payment, fubtraft the value of
5 guineas per annum, during the joint lives ;
and the remainder will be the anfwer.

Suppofing the joint lives, both 40, the
whole prei^nt value of the annuity in one
payment is, according to the Bre/Iaw Obfer^
vations, /.i-di^i, by Queft. I.-«^The value of
5 guineas ^^^^ annum, or of /•5«25 per annum,
during two fuch joint lives, is /•S^^S* multi*
plied by the value of the joint lives ^ that is^
5.25, multiplied by 9.82, or /•5 1*55; and
ibis fubtra^ed from Aioi.i, gives /.49.5>
the anfwer required for two lives at the agie
of 40. — ^The anfwer found in the fame way
for two lives whofe comtqpn age is 30^ »
/.46.5)*-»aad fbr two livts at 50, 50/.

Accord*

• Ac(!rordingtotheiL92u^/7 0bferVdtiob^»:fhofe
Values tire^ fof two liv& at )3o* /•54.6,— At
-40j>iL59,4*-^-At 5p, Al5 3^34 vi lit- i
! lf.the.firft,of tkie Mttual-paymehidris to be
-Inaderamqaediftttly^ itbcitroc aoiiffer Will^: in
ji^iwy itaftaooQi .be. \th«\ values^ iaand in: the
xaanoet j&ow difttAcyi^ aitiiinlflicd. fajr the .aI^>
au^r payoneni^lDr^ iDjitbo.:: pcrfent icaie^. .5
giiinttl:&£l th^affh^ jirilucs (p^ci&cd^
.; . The ,valu«Si^ do^^/^r^iwwnlf m^ annual ,fiayt^
t0ttin$St, of anj odbuDtr'x^ewi^i&iyiannuity^.wiU
bo arhmdk greater ,Qr:ldii tkadttbeicv as;th<»
anmiity itfelf is g][cator,p£.leJ(si. '.

I I

. . QjLJEalT ION VIj • — .

• • » p • I .

** A perfdn 3 5^ years of age wants 'to Diiy
** an annuity, for. what may h,appcn to ,re-
** main of his lif(R aftoar 50 years of age.
*• What is the Vflltie of fuch an annuity in
" readjf moriey^ s^fid 'alfo iii JiHnudl pdyrneht\^
^^ ^till he attainsL tQ the faid age ; that is, in
*' annual payments- foT' 15 years; fubje^ih
*• the mean time to failure, fhould his lift
•♦fair? / /

■ -' • A ft S \V E fti"

.. The -ptcftht ralne of :£uch in attOtfity Is
|the prtfent value of a life at 50, in ftioney to
.be>reMiviid.i5 yesirs hence, and the payment
of vfdiidi defiends on the contingency of the
Contitiuartceof the given life, 15 year's. That
is ; it is eijualr to the value of a life at 50^

C multi*

multiplkd by die prefeiit 'Vakii&.of . i A fo be
: received at the end ^> 1 5 yfeaii^ «id ilfd by

the probability that thevgivofii4tf<; ynH co^
nintle fo locig*-^A life aC 50, accordiiMg to
^MuDe'3fyim:ds^ valQaldoA d£ likres^ and teck-
-oAing iiitec0il:at 4 ^rr^. is worth 11*;^
-years poi^ctia&i TnelpiieiSsM valnejof: iiif.
;ta be 'received, at theicnd^of 15 yea^^ i$^ .by

Table I, <X5553« Aad4ke pbobabiiity tbgt
'8^ ll^fd'tt 35i vd'iXL contitt|ie'4 5 years^ it, ac-

- And t£efeL ^ three n^dbm, ^ nuUt^ied : byr oiie
another, give X4.44,: or tk$ number of 3reaffs
purchafe that ought to be given for the an-
nuity. — Thb annuity then being fuppofed
50/. .it^ value in prefent money is 22^2 4>

Y^/ The probability that a given life fliall continue.
• atvy niimbehof years, di-'v/t^ziii^z given age^ is (^s^ls
^Itfeii' known ),'i;be Fr^idioti, ^h^fe^frKmrrtf/^r is the num-
ber of the iiyinj^in any Tahleiof Obfervations oppofite
*to the gjyin age zhdJemmrwior, the number bppolite to
^the ^relent age'of' the gfven life— ^Thus, in the prefent
rihftance;.34^is the number in.Dr* HtfU^s Table opj^-

5te to 50|»^ aA|i 490 the ttumber. oppofite to 35«— "^l^. (^x
ie oHJs ot^i'j tQ 7) is, therefore, the probability. Uiat a
ferfon whbfe age is 35 fhall attain to 50, or live 15 years,
n the fame manner it wtii appear, that, according to the
fame Table, the probaEility that a perfon at this age fhall
,Kve tfjrVMrsj'^is ^| ; of nearly aa evcd chance*

At Northampton and Norwich a perfon at the fame aj;^,
has an even\(ihance of living 26 years:; but in Londtihj
'1tkitt\f %6 \ti^4 Seis •Tables III, lY, V, and VIII.
Appeodi^c. 1 will adc), th^i^ fof^eij^ tp .^my jM;e(fi|t
purpofe, that ^ perfon at the fame age has in tbefe towns
a bettef chance ef living one year, ukiA in Londffnj in the

proportion of j-ta*.

.. .-• *• In

kevirjiMary AtmiUites, &c; ii^

th order tb'fiJid t!hU >hilud lii dnnuat phy^^
• mentSj while the giVetf life U attaining to ^Oi.
iti^ttttdhtf to nrfd tHe value t)f an annuity*
for 1 5 yearsi fflbjiifl td failure tin- the esi-
tihAten of tAe riven Tift; And the value 6f
i\s&L aft a^ftuity ife^f ivi&ntlyt tfae lafli valuci
fabtrddted frorti the ^^ifite of tht given life j
oi^/itt tl» pi^fttrt ih^fbncci /.4.44i fbbtra€lcd
from i.i^.gy. (See Table VI, Apptfridix) that
is, /.'9;53,-»Js422/. tHen, being tW prefewt Va-
lue of an annikify bf yd/, for the i^mainddr
of a life ndw- 3^^, aftei^ attainiing to 50 ; and^
9.53 being the nuniber of years purchafe^
AVhich ought iQ^it gii^n for an annual pay^
iflcnrtb laft r5 yeafi^ if a life now 35 lafts
ihlxy^i it fdloWsi thd: the value of the iame
anntritv in atnitid paythents^ 'till this life
attdiiiS to- 50i- i^iSJrA divided by 9.53 ; or

TRit calciiltitwitii foppofes^ tliat the firft of
tiic aiinual pkymints^ is riot to be made 'till
the dud of a -ftTtCi If tfae firft paynlent iS'
ihdtitf immedi:iteiy^ th« value Will be^ thti^
^ngle payment divided by the valbe bP the HfcK
for the given term increafed by unity ; that is^
in the prefent cfafe, ^il A divided by 10.53 1
dr/.2i.o9i

f -t'

If <1m val(i«^ iki^^niiiiuity k i'eqiiiitd iil^
i fingle payment^ t>f tr and above^ tiiny given'
annual paymdht j[ d<iilud xht value of the an-^
itual payment frocii' the' whole tralue^iii a fin*^
gle prefent payxneiHt^ and the renMitadtr will*

C a bi

•» . '

20 ^ejtims cdficernmg

be the .an£w:cr;f — 'Ii hu^j. ict 5:^gttine9Sf Jb jCfae
prefent inftance^ be the given annual, pj^<<-
ment for the afligned term ; a^d lest l|ie cOr
quiry be, how much more in pre(0i;^t mpney
die fuppoii^ annuity is iworth. By whas4isi$*
been juft Taid, 9*539 multiplied by 5 guinfifm,
that is, 50 /• is the value of therannual pay^ •
ment; and this, fum deducted iroxs^ z^7,L
leaves 172/. the anfwer.

If the annual payment begins immediately,
its value is i9t53» multiplied by ,5 guin^as^^
and the an,fwer. comes out /. 166.7 c. .::r , . ,

•"1 <• r»

. In this way may be found the value, in
fingle and annual payments^of any other^an^.
nuity^ pajrable to an affigncd life^ after a^ngf ven
term of years, taking any {ValuAtionof\Uv,es.
or intereft of niop^y. \Butcare mui]^ bp (4^
ken to reimember, that it is the title to iho
annuity that will commence at the en^o^
the given term, and that the firft payoiept^
is not to be made 'till a year after.waf ds 1.
that is, . in the cafe here fpccified, not 'tiU*
tlie end of i6 year?. . / >

■ 'I

... SCHOU U M. .

The value of the remainder of ,t^¥6* j<^nr
lives, after a given term of years, is likcwife
the valujB Qf 1 A di^e at the eo4 of .the given
tP'iDf multipUed by the va^f: of two jpiPt.
lives^ each older by the given tcrin than*^
given lives; and this prpdii<ft,. multiplied bv
the prftlMSiiityi th*t th^ given joiijt lives fhall

■ ' not

.<

Revitflonary Annmtiui &c. 21^

'hot fiifl in tlie given term '; or (which is the
Va«c)^ bjr the 'produft of the two probabili-
ties,' ^tfiat the fingfe Kycs fhall each continue
^t gTvenf term; And the value of an an*
nuity, on any given joint lives for a term of
years beginning now, is this lail value, fub-
tradled from- the -whole prefent value of the
jointlives. Thus; thevalue of two joint lives,
one 40 years of ^ge,; and the other 50, (fee
Tabic VII,) is 8.91; which, multiplied by
.0,6755, the value of 1 7. due 10 years hence,
and by fJo (the probability that a life at 30
/^^l continue 1 o years) and alfo by -^^^ (tht
probability that a life at 40 fhall continue 10
years) gives 3.92, the prefent value of the
remainder of two joint lives, aged 30 and 40,
after 10 years; and this value, fubtrafted
from* 10.43, (^^^ value in Table VII. of two
Joint lives, aged 30 and 40) leaves 6.51, their
valufe for \ o years.

•; As the value of the longeft of two lives is
'always the value of the joint lives, fubtradcd
from the fum of the values of the two Jingle
lives ; their valu? alfo for any given term^ is
the value of the joint lives for the given term,
fubtraded from the fam'of the values of the
^ng/e lives for the given term.

The truth of thefe rules may eafily appear
w.ilihput:particular proof. I have, however,
lyQifilQd ovu the method of demonftrating
jhem it\ ^ npte faj at the end of this work.

'--{a) Sec note (B) in the Appendix.

C 3 By

4M ^^ioiu cofKfrttkill^

By Bscaht .cfteration*^ in^y btt fopn^ -tb?
values of. 3 pr xaf>xem9( lives, pr the lopf^
pf /i!r«^. or more lives, for a jgivefi tsri^ vi
years, or of what fliall.f^^ pf tfew Wfef
^ givpn tcfm pf yeafs,

• • • '

*' The prcfent value is requirtd of an an^
^^ nuity to be cryoyed by onS life, fpr what
^' may happen to remaiA of it beyond apo*
f^ ther life, after a given terni; that is^ pro-?
*^ vided both lives continue, from the prer
^' fent time^p to the pnd of ^ ^vcft f erfn of
'* years ?

Answer.

■

Find the value of the aneuity for two }iyci(
greater, by the given term of years, than tjip
given lives. Difcount this va^up for the gir
ven term ; and then, multiply by the pro^
bility, that the two given lives (hall both
(Continue the given tefm; fpd th6 prodi^^
will be the anfwer.

E X A M,P L E. .

Let the two lives be each 30. The term
feven years. The annuity 10 L Intereft,
4 per ^^«f .-— The. given lives, increafed by
7 years, become each 37. The value of two
joint lives each 37, is (by Table VIL) 10.25^

The

'ReverJ^aty Annuities ^^^c . i ^

Tbe'viluc of a fioglc life at 37, is (by Ta-

,b*4 VI.} 13.67. Tfteformcr; Mtrai^^

^^lafter, is 314^;. w Ithb' vaJae (jf an annuity

Ibf tlic Bfc of a pteiferl 37 y^ars of age, after

iilother df the' fanie age, byQiteft. L-— 3.42

llrfix)iintct3 for 7 years^ (that is, multiplied by

^^7^, the value of i /. due at the ehd df feveii

yeata, fey Tabic I.) ts 2.6.-^The probability

tiirat a finglc life at ^30 (hall continue 7 years*

ts (by the hypothefis cxrilained page 2.)

Vis' fa). Tht probabHity, tnereforc, that two

V - . ' '^■*\' fuch

■ *

w ...

{a) In this cafe, it is on Tome accbahfs beft, as wdl
«$ ^afieft^ tm take ilie pfohaUiims of ii^ fmrn^tfae hypo*
tbefis, rather than jmipedia^telxA'Qm the Yahk^* — Fifty-*
ifix perfons being Cuppefed alive at 30, pn,e will die every
year, according to the hypothefis. * AtUlie'ertd of feveh
f«K8 then* tCr attiabqr of the Jiving^ W^l t^4^, and ^^^
or the odds of 7 to 1, is, by^ot^S*. l^y'tlMj^frobaVlity^
that a lift, aged 30,' wHI continue n years ; and this frac^
tion, multiplied by itfdf, is the prooability^ thatti^o Iiv6l
'fii£ tki««|gB^iludl J^d'cniMailW 7 <^ea^^ In general, it
jnitft be j^iAfloaberedy tbfU ^ pf pUib9jjEK» t^at ^pf two
.or more eveqts iKall all happen> is thr pio^fSb af ifing from
multiplying" by one ^nbther, thft pifobabilines of all the
events taken ieparately. The probability, therefore, that
9iily .nnahfer of perfons vriil Jii/ lite any'giveti time, it
jrigbtly found by imiitiplying into one another the proba-
jNlitiea that each of them will Iht tluir*tiine,^^lt may
iunb^r bq of life to fomey dwt I Abuld obferve bene, ^hat
tlie difference between um^and lAie fr^Aionexpr^ng
, ithe pFobabilrty, thait'aa event will ha'{])Mn, gives thp
-probcifaility that.it will nrt happen.' Tim ;^e pF(>babL-
Jity^ that a person 40 years of ^ge witt IKre if years,
Is, by the Brefiaw Table\y4. The prcfbability, there-
fore, that he will not live 1 1 years, is ^^ uibtra<£ted

C 4 '; ' - ^ ^ from

^4 ' ^Jtm^ omcemmg

fuch lives fhalL both continue 7 ye^s^ris
7TT7# or, ia decimals 4^.765; And 2;6/fiii4f
tiplied by Of765, is 1^9, the nuqiber^qf.
y^ars purchaf^ which oiighc lo be given for
^n annuity^ to b? enjoyed by a life now 3Q
y^ars of age» aftpr a life of the fame age, projr
yided bath continue 7 y^ars. The annuity
then being loL its pr^fept value is A 19. 89. 7
^ By iiniilar operations, it piay be £bundt
that fuppofing the term one year, and the
^ge$ and the rat^ of ipterefl the fanfie^ th« '
prefcnt value of the fame reverfionary an-
nuity is A32'.4; and that if the term is 15
ywrs, , the. value is A 9,7, .

For two lives each 4o> thefe values are
/.30.3-3- -^/.i744. -^7.7.3, the, tsrip being

For two .lives each 50, the fame valuta
for the faitie^'ttrfn^, are /.28,2, — /.13..86,--

/.4.34/'^/ ;\ , '. ^-y, . ,;. :.. .

, Thef^ values, according to the London Oh^
<ervation« and Mr. Simpfoit^ Tables^ of the
values of firigle and joint livqs* arc, .

»' • •

from unity or ^^. — In like roanner : The prorb^biiieytbat
two perfons aged 30, (hall both live 7 years, being 0.765:1
the probability that tbey wW^noi both live fo long, or
-that m?€ or Hher of theoi wiil 'tbe in 7 years, is '0*765>
fubtracied from unity, or .235.

If any reader is unwilling to take thefc affcrtrons for
granted, bp (hould confult the beginning of iVIr. Dt
jW»ivri\ ox Mr. Simpfott*9 Tfeatifes on the Doctrine of
Chances, where .he will find theih demohftrated,

(a) See^Note (C) Appendix.

For

Revef^/kfUfrjrAmttiiites, Sec. 25

: »

I

«

for a lives at 30*^A32.05— A18.62---/.7.66.

: :- at 4c--*/.30.7. — •/; 1 5.6' ■~/.5.45.
. : ^ ttt 5l>W.89.36-^— /.I2.^3— ^.3.24^

Qj; E s T I o N VIII.

•* Let the fcheme of a fociety for granting
*' annuities to widows/ be, that if a member
'** lives a year after admiffioh, his widow.fhall
5* be entitled to a life annuity of 20/. IF
'^^ Jeven years, to 10/. more, or 30/. in the
*' whole. If fifteen years, to another addi*
*' tiohal io7. (Jr 40 A in the whole. What
V. ^Vg^i ^^ ^^ the annual payments of the
*** members for thb ages of 30, 40, and 50^
** fuppofing thfe-m bfthe fame ages with their
«' waives, and allowing compound intercft at
** 4 P^r cent. .?

Answer,

According to the bypotbefify ej^p)ained
.p. z; and, therefore, very nearlyi according
.to the Tables of Obfervation for Brejlai/a,
.fioru^'cb, and Nortbampton^

/. 8.44 — /. 8.69 — I. 9.05.

According to the London Obfervations,

• « • mT

" /. 9.4,1 — I. 10.17-?-/. 10.92.

■ ' ^ Thcfe

Thefe values arc eafily deduced from the
fdiicj in the JUft Qsseftioii. For cxampk.
The iralue of lo ^ per anMum for life to 40
ifter 40t proyided the joint lives do not fail
in^ Qfie year, is, according to the bypotbejis:^

^*3^*33* '^^^ value of ^o l. per annum^ m the
fame circumfhmces, 1$^ therefore, /•6o.66»-*^
In like manner^ the value of 10/, ^vtvjtveM
years^ is A 17*44^ And of 10 A after 1 5 yeais;
/►7.3,— !-Thefe values together make /.85.4, of
the value of the expei^ation, defcribed in'thi;
Queftion, in ^Jin^le prefent figment j which*
divi4ed by 9.^^ ^the value by Table VII. qf
two joint lives at 40) gives iJ&.bg^ the valup
6f the fame expectation in annual paymenH^
during die joint lives 4-^In the fame manner
may be foiind the aniWer in all cafes to any
Quejftions of this kind.

Thefe calculations fiippofe, that the an
nual payments do not begin 'till the end
i year. If they are to begin immediatefyt th^
true annual payments will be, as was before
iihkt^tii thtjfngk payments, divided by the
value of the joint lives increafed by unity {
and in the prefent cafe they will be, by t|i6

hypoth^s^

• -

/, 7.75-^/- j.gr^L 8,07,

^y the London ObferyationSji

/. 8.52—/. 9*06—-/, 9. 51*

%

' ' Bf ib^ ifiethod of calculation bow eic-
^^nedt may bp ' e^^iy fmwd ip all fafet.
iiippofi«g toe Mnm^l payments previoufly^

(rorrefpoi^ding to thtfn in v^tie.-mTbns, ibc
^miitics being the fame with tbofc mctttb-
f)fie(i in thi^ Q^eiUop^ the tman annul piy*-
faents for all ages between 30 and 50, are
nesirly 8 A aqcording to the bigheft probtbi^f
Jities of life 1 9 A according to the /(»wg^ $ and
iS gpineas the mtdiuvt (0) ; intereil bein^ at
4 fer cfnt. and the fim payment to be made
immediately.

, If the mean annual payments^ beginmng
Immediately^ are fixed to five guioeaSt the
^orrefponding life annuities will be .nearly
/by the hyfgtbifis) 12 1, if the contributor
j^ytf 9 year» and 24 /. if he lives fcven years ;
IK ( by the London Obicrvatioos) 1 2 A if he lives
^ ywf, «id apA if he Jives fpven ypars fhj.

It

- (tf j Tbe vahie of 't)ii$ «xpe3ftciftnf fipfpofing mtrrM
IDeo 40 years of i^gf:, an4 tb0fr.wjv^s 3(0, is, in zfinrk
|Kiy ment, 113/. Jaanim^ p^jpfients, b^gmning immeoti-
aMly» ;/> 9^S8^ W the hypt^Jtt. And 107 /.—and /.ia93»
by ^ -Iton^n. Obferv^tioas.

' *^7.^j:hc aonMitics in c^^^geftatipn arc 14.^ provided f
in^rojSeLXiyes a year, ^od 20/. provided h<^«Uv^ ftvca
jciars^,tbe proper mfavJif^U gayp^xiis fpr (^age«, takca
fine 'with ^t^er, under ?.q 0^*50} is 5P gq^i^iaa i^arly^
ific^Qr<Jing 'jo . all the .TsiWo5 ' ii? Qbfo-«^a;ioA, . (iippoTiBg
Muafiiy of age between p\wi ^ipd' their wivca, Apd the
aacTuibn wlii'tb ought tor be made,. on 9CCQU|^ of e^eif
pf age on the man's fide is, taking the neareft and the
•.:j::i eafieft

' It is ebfcrvabic, that xht differemrt iD the
.values of the ^hnuilks^ aiifing frbrii' difl^-
r<eflOf~of age»9 afld the difierence in the pro^
babilities of life> is lefs in this Qneftioh than
in* Qwilion 4th 1 an<^ that, confequently, the
plan prepofed in it/i^ the fafeft, as well as' the
ineft 4Bquitable andencotimging, that a fociety
can adopt. ^*

* It is iieceiiary v> remark here further/ fhsft
yearly payments which begin immediately^
are more advantageous than half-yearly pay-
ii:ient$ which begin imn>ediately . Mr« SifHf^
fon (in his Treatife on The DoBrine of An*
matiis and Re^erfions^ p. 78, and alfo
in^Alf Sele£i Exercijesj p. 283.) has (hew»>
that; in the cafe of life annuities, half-yearly
|]dyments, which* begin at the end of half a
year, are 4 of a year's purchafe better tham
yearly payments, which begin at the end of
a year^ And it is manifeft, that balfryearly
payments^ which begin immediately, are no

cft$ieft round fums, aSout a guinea and \ fbr every year
a3^br as 17 y^ri; or, in the annual payments, (lup*
•poTed 5t guineas) \ a gufnes^^ mmum for five years ex^
.{^, add 4 s guinea more for every four years excefs be*
yond five ^ears, 'till the exceft comes to be 17 y^rsv
And^ I beheve, that 60 gvimeas 'mJmgUfajminti^diidfix,

of k^'hktiffcih them arid their Wives, the annuities be-
In^ alfalongftippofed' X6 *e ///J annuities*' and inter^ft
pxkihiidWl per cmt: .' ? \ . *

-...'n moro

more than half a year's purchafe better thaa ^
thofc which bcgiiijat ithfl fP A of half a year.
^Mjiearfy pay«ieijt§, .^hich b^in immedi-
ately^ >rc a ^Jlfole years' pur^jiafc better *than
the f9fl^e payments , to ' begin;' at the ^tkd of a
yc*,r. , The, 4iffer;^ce. or value/" thirtfofe/
^tweeii. y^(irly\ aiia baff^ieariy paymfcttts/
^'ppofiiig bojth to begin, immediatelyt is a
quarter .ofXy^^^'s purchaie^in favour tff thii.

^ • i ill

• • • #

' QjJ £ 8 T I 6 N IX.

^''iTie value' IS required of an annuity to
•be efijdyed for WHa< may happen- to-rc-^
maiA bf one lif^ aft^r another^ provided

^^ the life in expeftatioh continues a givea

** time?" * . ' -

.1

♦ *-

An S'wfi It. • ' '•

• * * • '

hiy -Qadlion: VJ. thfc prefent yAlue ci
the aftinuiit]^ for the: .remainder of the Mq iiQ
expedatiob^. after thfi^vtux timc» avd.myltir
ply this value by the probability^ that the
ether Itfe'fhall fail Within tbs!€ time, r Fi&d
alfd, by Queftibn VIT, the value of the rever-
iionj^ prpvided both lives continue the given
time. Add thefe values to one another, and
the Jiim will be the anfwer in a fi|yglc pre-
fe&fpaymcrtt.

>

v.* , ♦♦ 4

An annuity of *i o /. for the life of a per|btf
how ip, is to commence at the end of il
years ^^^,,1? another p^ now 40^ fhodld"
be. then aead; 6r^ if this fhould not happen>
at the end df any year beyond 11 years irf
which the former (hall happen to ftrrVive thtf
latterV' What' is the prefcnt valoeof ftfch aft'
annuity, reckoning intereft at ^per cehf. itia
taking the probabilities of life as they are in
Dr. Halley's Table ? ^
-:TJi© y#I«e of \o l^Per unMum, for tfic.re-
m^in^r.oif the life of a perfon now 30, aftee
1 1 .yeaF$> fouad by C^ft. VI. is /.6g^j.'-^
7he probability that a^ p«xfon 40 yeans of. age
(hall live 1 1 years, is, by Dr. Ha//e/s Taiblc^
-Ut* The probability, therefore, that he
will 4ie in 1 1 years, is ^If fubtradted from
unity (^), or ^^Ti which multiplied by/.69,43,
gives^^ A I ^rr6*-*-The. value of tfic reveriibn,
Movided 0ofi> live 1 1. ycars^ found; by C^efi^
VlL )s 17 /; Aad dxi» talud added to the

(oX That is, the title to die annuity Is toc«in«ieic«
• at die end ^ 11 years,, anithrrfirft payment to bf made
a year' afterwards, in cafe th\s, life in ex£edation fhoixld
cotitimie Tor long, and the other fail. But if htklWei
fliottld GDAtitiue the givtfttemif the-fitft* payment is aU
ways to be made at- tl^e-end of the-yeat}- in which^thf
former life iball happen to furvive the latter. See Queiiy
VL •

fii) See the Note, p. 23%

ionxiefj

Tormer, tMkts I. 34«96f the value >e<|tektr6f|
in a Jmgie frefhtt p^^mti ifrhkh jiaylttent
divided by Lii.^%i (the value by Table V^L
of two joint lives^ «ig^ 30 and 40^^ WitH
unity added) gives 3 /. (a J i or the vfchie re^
quired in annual payments during the joint
lives^ the firft payment to be made tmtnedi-
ately. — If, every thing clfe being the'(amei
the affigncd ferni is 15 years, the value re-
quired will be 29/. in ^ Jingk payMenti and
L7,.^^*m annual payments.

Que s t I on X.

^ What money in hand, aitd alfa ia an^
^* nual payments dwing life, ou^t a perfon
<' of an aiSgned age i;o give for a ium of ipo^
*• ney, payable athis death to his heirs ^^>| ?—
<^ In other words, what money in handif ^Q^
*^ in annual payments during life, ought a
" perfon of a given age to pay for an ^^*
** raiifc of any given Sim on his life ?**

Answer.

Subtrad the value of the life frdnv the
perpetuity. Multiply the remainder by the

*

(a) See the demonftiataon of this riHe iii» Note (D)
Appetidix,

{b) This Queftion is the fame vritfa Problem ij5lh, ia
Mr. D/ Mww$\ Treatjfe oh Annuities, and Prabiem
a6th, in Mr. Simpfitfi Sele£{ Exercifes ; but the anfwers
there given are right only when applied to reveriionary
iftatet^ and therefore muft be materially wrong, when
applied to reverfionxryyirivi, as will appear from the Sch^
to this Queftion, and from note (£} in the Appendix.

3 prod u A

52 . . ^^ui €$ncermi^

pro4itt<a qf^ t))^ given /mn iiUa th« int^rcft .flf
ioo/ for:9[jrear :. and. this laft prodtt^y dji^
vid^djby \ooL in^ix^i^ by its intereft for. 4
yt?^ will give the apfwej in a ;^i!ig^/<f prefect
pay meot. And this p^y meojt; divided by th^
yalue of thejifc/ wiU givie* thci anfwcr in an^
nuaf: ^pfffmcutf, dunqg the cgntinuanqe , q(
thelifcji., , .

£xj|^ple«, L^t the^liiib b? 30. The fufii
jioo /.^ iThe rate of intercft 4 j^^r €enf* AncJ
the valuation of lives,, that in Table VL Th^
perpetuity, therefore faj, is 25. The inte-
reft of I op /.tor a yeaf, is 4 /. 1 00 /- injcreaf-
cd'byitslntcreft^for 'a-'year, is 104/.' And.
the value of the Hfc i4.68, — The value of the
life, fubtratSted from the perpetuity^ ' gives
1 0.3 2-,. which, multiplied by the produ(fl ot
iooA into 4, or by 40b; gives 4128/ And
thi^, 'dividdd by* 1 04V gives 11 39.7, the va-
luer of x 06 A 'paysfble at the death of a perfori
aged j6,''!rf*a' fingld'preftfit' payment.— And
this payment, divided.by 14.68, is /. 2.7, the
fame value in annual payments during the
cpntinu^ijijfe of the Jife*

Thefe values found in the fame way agree-'
ably to the valuation. ofriiv.es. for Londorti in
Table X, are l.^^.jt^ and /.3-49. — If the lif«
is 36, and intereft a^ferceht. thefe values arc
43 /. and /. 3.1, by Table Vl^ and /. 49.6*1

.' . • • ■ ' • . . • .

{a) That is; the value of xk^z fie-fimpU of an eftat^
found by dividing xoo/. by the rat^ of in^ereft^

an4

. Rever^naty Annuities ^ occ. ^ j

afid /.4;i; by Table X.— If intereft is reck^
bned sr^ per cent, the fame values are,~"by
Table VI, for 30 yeaftf of age, /. 48.14.— ^
2.86. — For 76 years of age, /. 51.43, and

It appears here; that difference of intereft
makes no confiderable difference in the anf-
wers to Queftidns of ihls kind^ except when
the values: are required in a^fingle payment.

If the iirft of the annual payments is to be
filade inimediately^ thb fingle payment is to
be divided by the value of the life, with uni-*
ty ad4cd to it, agreeably to v^hat has beea
jLlrea4y olifervedj anjl the annual payments
iOL this cafe (intereiL fiippofed at 4. per cent.)
^iltbe by Table Vl, for a life at 30, /.2*53— *
At i6t A 2.Q<

. If th? payments arc half-yearly payments
begiqning immec'iately^ |he fin^e payment
mud be divided by the value of the life in«^
creafed by ^, or .j^, (fee Queft. VIIL) And
the half-yearly payments, for the age of 36^
Avill be half .2.9, or 1^45. And half 1.45^
or *7?5, lis iikewife nearly the proper quar-
terly paymeivts.

Again ; if an annual payment, ()eginhing
immediately, of /. 2.9, ought (reckoning in^
tereft at 4 per ant J to purehafe ^oo/. pay-
able at the failure of a life now 36 ; 5 7. by
the rule of proportion, ought to purehafe
,172 /• And in like manner, it may be founds
thjit the fame annual contribution, in half-

D * yearly

1

34 flgi^ions concerting

yearly or quarterly payments, beginoing iiii«
mediately » ought to purchaie i7Q/.-«-Tb^
fum$» according to the London Obrervs^iont,
are 132/. and 130/. nearly.

The reafon of mentioning iheHb partial^
lars will be feen in the next chapter.

Scholium.

If the reverfion is not a Jhrn^ but an an^
nuity for ever, or an ejlate in fee-Jimple^ tb be
entered upon after a given life, ita prefenl
Value, Z:^ a Jingle pay menty will be •* the value
** of the life fubtra^ed from the perpetuity^
*' and the remainder multiplied by die an-
«• nuity, or the annual' pent of the eftate/'— ^
And the value, in anrtudl^ayments^ WiH l>e, ai
before, the fingle payment divided by the
value of the life. — Univerfelly. It oujght to
be remembered, that a reverfionary ejlate^
after any given life or lives, is worth as much
more than a correfponding reverfionary j^/»i
as 1 00 /. increafed by its intereft for a year„
is greater than lao /.—Thus, the pfefenf va-
lues, in iingle and aniiual payments, of 4/.
fer annum for ever, and of 1 00 /. in money
after -oxtj ailigned fife, are to one another^
(intereft being at 4 fer cent.) as 104 to 100,
or 1 .04 to I .—The reafon of this difference
is, that the calculations fuppofe, that the re-
verfionary Jumf and the • firft yearly rent of
the efiate, or firft payment <tf the annuity,

3 arc

4^^ to be raccivec} at tJbe fame time, after thtf
jUX^ad;ion of t^ Uv^s jn ,poire/1]on« Iti^
«i|iy to iee^ thaf this is a circumftance which
^ufl make the latter of mod v^lue. But to
4ypve^ ^ny xloMt>t6 about it, I Q^\\ explain
Jt more particularly in^ a n^e ia the Appenf

Qj? E dT 10 N X|, .,

^* A perfon of a-giveii age< hatnng iyeaf-*
*^ ly income which will fail with his lifei
^* wants to make piribviifion for fcnother per-
^* fon of a given age^ in cafe the ktter /hould
'* happen 10 furvive% What ought the for-»
^' mer to giv€ in n &Qg\t payment, and aliof
*^ in annual payments during their joiot lives^
^' for a given fum^ payable at his death to
•^ the latter ?

It is roanifefti that the val^fe of the g^iven
fum in this cafe^ muft be lefs than in the cafe
ilaced in the laA; Qjgeftion ; becaufe^ here the
payment of it is fo&iended on the eontingen-^
cj', that one life (hall furvive another, where-
as in the other cafe^ it is certainly to be paid
at thd failure of a given life^

«

t^ind, by the folution of problcfh 32f(!y
(p. 297, Mn Simp/on'a Sek^: Exetcifss, tha

(aj Vid, Appendix, note (E)^

Da- taluef

'*

36 ^eJiiMs eoncefn$j^

value of ah eftate, correfponding to the giycn
furo, and depending on the given furvivor-
fliip. Divide this value by i /. increafed by
its intereft for a year, and the quotient will
be the value of the given fum in a (ingle pre-
fent payment. And the fingle payment^ di**
vided by the value of the given joint lives,
will be the anfwer in annual payments during
the joint lives.

The folution I have referred to Js 'as fol-
lows. .. -^
Find the value of ,30'. annuity, on tWQ
equal joint lives, whereof jthe common age
is equal to tl\e age of the older of th^ .two
propofed lives j which value, fubtradl from
the perpetuity, and take half the remain-
der. , Then fay, as the expeSiation of the
*^ duration of the younger of the two lives is
** to that of the elder, fo is the faid half re-
*^ maindeir to a; 4th proportional, which will
** be the number of years purchafe to be gi*-
** v^n for the eftate when the life in expec*
" tation is the oldeft of tbfe two. But if this
^^ life is the youngeft, then add the number
*' of years purchafe jufl found to the value
" of the joint lives, 9ad let the fum be fph.?
** tra<£ted from the perpetuity, and you will
** alfo have the anfv^er in this cafe (a).''

■ . • Let

' (a) Mr. Simp/en hzs given the follbwing examples of
this folution, adapted to London lives.— Example I.
*' Suppofc the age of the expeHant to be 40 ; of the pof-
^^ fijjpr 30. The rate of. intereft 4 per cent, and the

« given

€i
€€
€€
€C
€i

\

Rever^nary 'Annuities ^c. 37

,' Lftt'the.life in'exfieftStion be* bo ; and the
oifccr life 40: ■ •The fum,« 100// -Intcrcft;
d^ per cent. ^ Tht valuation of lives; that in

^)xt fxpeBation of the firft life, h 2??; of
the^lecond life 23, by Mr. De Moivre^s hy^
fothefis: The villjeW the joint lives is 10.4.3,

*'. pHtn legacy 5000 V, or 200 1: per amum. Then the
^ value- of. two equ4 joint lives of 40, being 8.1, by
M Table XI, and the perpetuity 25, the remainder of
" difference will be here 16.9 ; whereof the halfis 8.45.
>•* Therefore, it will be a> 23.6 to 19.6, fo 8,45 to 7.02
y years purchafe, or If 1404, the required votue,^

Example II, ** Let the, age of the expeSlani be 30, of
** Xh^'pojfejfor 40, arid the reft as in the preceding exam-
« ple^ Here the value of the joint lives jb'ai^d 40, will
^' be 8.8) which add^ to 7.62, (found above) the fum
*^ Mfill be 15,82 ; whence the anfwej:^ in this cafe, is
** 9.18 years purchafe, or 18^6."
' I have ihewn*, that the values of reverfionary ejiateiy
and reverfionary fums^ are not the fame as' is here fup-
pofed, — The rale gives the true value v/hen applied to
the former; but, when applied to the latter, the values
given by it muft be divided by i /. increafcd by its inte-
reft for a year, as abovef direded.-^The fame oofervation
is to be applied to Mr. Simpfctf% next Problem^' or the
^3d. • J

. In thcfe Examples 23.6 and 19.6, are the expe£tations,
in Table IX, of 30 and 40, according to the London Tab-
bies of Obfervation \ a|i3 the method of finding them for
any age, and from any Tables of Obfervatign^ ia ex*
plained at the beginning of* the firft EfTay.

In Mr. De Moivre^s ^pothefis^ the expedlation of a life,
IB always half the cmipleoicnt. See note, p. 2.-^Some»-
jtinies the complement of a life is mentioned wit)iout any
view^* to Mr. De M^ivr/s hypotheils, and i( then means
double the expeHatiirt of the life, whatever that may be,
according t% mj Table pf Obfervations,

D 3 by

3^ ^^J^^^ ^^^cernlflg

by Table VIL The Taluc of two joint lif cs,
both 40/ is 9f8^9 by the fitne Table^ Tho
cflate correfponding to 1 00 /. }s 4 /. ^r mtth
and the prefent value of fuch an eilate to be
entered g:pon by a peribn 30 years of age j pro-
vided he furvives aperfon ^dO.yeafs of ag<». fit
by the rule juft quoted, /. 3J.3»*. • Aadjthb
value, divided by i /. increafed by its intereil
for a year, or by 1,04, is /. 3a>03, the va}uft
in z Jingle prefint payment of the fnm of 100 ^
dependent on the given furvivorflhipt , And
this fingle.. payment, divided by 10:43, ^^
/. 3.07, the required value in annual payments^
during the joint lives, if the firft payment i«
iiot to be made 'till the end of a year* Boit if
the ^ft paymoit is to be made immediately,
the required value in annual payments will ^5
If 32.03, divided by i i.43, qr /-a'.S.-r— Thefa
values, accordiJ3g to the London Obfervation&i
or Mr. SimpjM\ Tables founded upon them^
^re /. 35*30, in ^ Jingle payment^ and /. .3.6, ia
fnnu^l payments^ beginning immediately*

Mr. ^impfony In the Problems following
^hat here quoted, has given folutions of mofl:
other Qucftidns, concerning the values of re-
vcrfions dcpcndirlg onfarvivorfhips, where
the whol? duration of two pr three Jives is
cpacerned* And I am acqoainted with n(i
other folutions of thcfe Queftions, wljich are
applicatfle to all Tables of Obfcrvations, and
fyhjch at the fame time (proper regard beings

paid

psM ft) the corredion explained in the lail
Qoeftion) vnKy be confidered as fufficiently
corre(S /^a^.

Qjl E s T I O IT XIL

. *' Suppofe an inftitution. for the relief of
^^ lAridows to. extend its affiftance likewife
to the families of married men, provided
they Icaye no widows. Suppofe, for in*
*^ ftance, that in this cafe children are to be
*f entitled xp loo/. What is fuch an.cxpec*
** tation worth, in prefent payment, accord*?
" ing to Dr, Halley'^ Table, intereft being at
^ 4 per cent, r

Answer..

■

If 40 is the jxiean age at which members,
are admitted on fuch an inflitution, and 3a
the mean age of their wives, the anfwer
(fuppofing no fubfequent marriages) is, by
^^ %3^ Problem in Mr. Simeon's Sclo^ Ex-
crcites, p. S98, and the corredion already
explained, l^i^.^ofij.

3ttt

(a) Sec the third Eflay. ,

(b) This Probicm and its folution are given hy Mr.
Simp/in in the toWoyrltfz wordt : *^ A and his heirs are
^ entitled to an eftaie of a given value, upon thtdeceafe
^* iff Bv provided fi furvivea A ^ to find the value of
** their cxpcAation in ^tf/^ff# money/' — Solution* "Find
^* thcr value of an annuity on the longeft of two equal

But there is a redudtion necefTary; ^on ao-r«
cpunt of the (:hance there is,:t)iiat a widower)
may marry again. Suppofe, therefofc^ on?j.
half of all widowers to marry a fecond an4
third time, apd that two-rfifths of fuch wid*
owers furvive thcfe fubfequent marriages. In
this cafe, i added to t of -J* Or ,V of all who
become widowers, will die without leaving
widows, and therefore /-er of A 13.8, or /. 9.66/
will be the anfwer. If only one fourth of
all who become widowers marry again, 'and
two fifths of thefe furvive, tl^e anfwer wilj
be /. ix-73*

^* lives, whereof the common age is that of the ol^ej* of
f* the lives A and B -, which value fubtradt from the

perpetuity, and take half the JXifiainder ; then it will

be, as the cxpedation of duration of th^ younger of
•* the lives A and B, is to that of thp pld^r, .fo i^ the
•* faid half remainder' to the number of years purchafe
** required, when the life of B u the oldir efiht tivo. BmV
'^ if B ke the youpger ; then to the numbier thus foutKl>i
^^ zif\ the value of an annuity on the Jongeft of the lives.
*•• h and B, and fubtraft the' fum from the perpetuity j^
•* for the anfwer in this cafe.'* ^

If th^ xftate is 4 /. pir annium^ the age of B 40, atid df
A J2, intereft 4 per cent, the apfyver by t^iis rulecomfs
out L 14*35) which divided (as in the pi^ceding Qucftidn)
by 104, gives /. {3.8c, the value, as above, of 100 /• in
money. If B is 30 and A 40, th^ fame yalue is 20/.

N. B. The value of the longeft of two lives is always
the diffirence between thtVaJuc of th^ joint liv^s, and the
yi//i. qifihe values of 'the twogiycn JiniU livcs^ : Thus i
the value of ,a Ji^e at 40, ia, by Table VI, 113,2. The-
fym of the values of two fuch lives, is 26-4. Tbfe value-
qf two joint lives, whofe common age'is<40, is, by Ta-
bjje V^II, g..82 ; and tiie dijFerencc is 16.5?, ox the valua
ci* the /oMge/? of two lives at 40'.'

This

Jtevfj^frmary jinnuities, ^« 41.

This calculation fuppofes all marriages to
leave children who furvive their parents. If
tbis,i$ confidered as uo&ei;tain, the valujes.iiow
determined muft be dinynifhed iri. the pro-
portion of*, this ' uncertainty. — Tliusf if.ojpc
niarriage in feyen f^ils of leaving; cJ^fUlren (aj
that furvive their parents ; thefe V^lwe? 'wilt
be. reduced a^wj^/A part, or to ASi^^^V^f ^^^
ancj A 10,05, if J. quarter pf all jwidbweK

nvarry, w . -. ^^ .. . . ...

In this way majj isuiy other qu^ftions of the

fame kind be anfwered on any fuppbfitions

that way be thought jupft reafonjibic^

,.QuE§Tl,q^N. XIII.,,.;... -.. ;

- *' Let ft« eft2rt)Kfiimcnt be ruppo(fJd^5^hich
^ takes in at once all the mairriages- in a*
V coutttry, Or -fttt marri-ages arfloftg' pterfons
^* of a particular profeflion within a given
♦* diftri&, iarid fubjefts them for perpetuity
^ to a certain «qual and comm<!m' tax^ or an-
^* nual payments, in order to provide life an-
•^ huitiesfor fueh widows as fliall refult from
^ thefe marriages.- What ought ^he tax W
*^ be,' fuppbfing the annuity 20 /.'add calcu-'
*^ latiiig at 4/^r cent, from Mi*. De Moivre^s^
*^ valuation of lives 3 or, which is nearly tha
*^ fame^ from the probabilities of life in Dr.
« Hafley's Tablfe of- ©bfervitions ?!* • '

< . • . '

(a) This for vf^s^y ywf ha^becp nearly the fad among

^e (uinifters and prQfefTors in Scotland.

Answer*

A VS W£ K.

Since at the commencement of fuch an
eftablilhhieQt, all the oMeft, as well as the
youn^e^ marriages, are to be entitled equally^
4d the pfopofed benefit, a much greater num«
^t di annuitants will come immediately tip^j
tfi it, than would come upon any limilar
eftablifhment, which iknlted itfelf in the
admifiion of members to perfons not exceed-^'
ing i given age. Thi» will check thjat ac-
cumulation of money. Which fhouM take
place atl^VfV, in Order td produce anNiiicome
equal to the diiburfements at the time when
the number' of annuitants comes to a maxi^
#f «»i l.and^ therefor ev will be a-particulaf bar-
den upon t^e eftabMfliment in its infancy. Fov«
fbts, iome compen&iioa mmft be provided 9
and the equitable jnefhod of providing it, is^
by levyipg^i^^j at the beginning of the efta^
Uiihmenti on every member exceiding a gi^-*
ven age, proportioned to (he number of year»
which he has lived beyond that age. Buti iii'
the pie£^nt queftion^ it is fuppofed, that ^k^
fioea cannot be conveaieMly levied, or djiat
every payment muft be eqpal and comnMny
whatever di^arity there; may be in the vatu^
of th^ expQ^tion$ of different members
The fines, thereforie, niufl .be. reduced to ono
common one, anfwerine as nearly as poilible

tp' thdi di&dvantage i Have mentioned, and

^ayabler

payable by every nembdr at the thni when
the eftabli^bmeiit begins. After thi$> the
eftabiifliment will be ^e fame with one tfiat
takes upon it all at the time they mwry^
and the tax or annual payment of every meca^
ber akjequafe to its fupji^it^ will be the aanO'-
al payment during mafris^e, due from perfdm
who marry at th^ mejin age 'at whidi^ Upon
to ayer^9 all marriages may be canfid^ed
as coaunencing,-~-There are then two poiimi
to hb here determined; Th^Jines neceffary to
be Mid -at firft, according to the account i hat^
juK given ; and ih^cii^ant annual payment ^
netefi^fy to be made by every member, at
«n eqfuivalent for th( expe(3ation provided
1^ the eftaUiHiment^-^l^fae ^jf9^ to be paid
fX firft ares for ev^ry particular member, the
fame ^tth the differefjee between the value
of the expe<Sfcaiion to him at his prefent age,
and what would have been its value to ^m
tied the feheme begun at the time he marri^
cd? Or, they are, for the whole body of
jnembcrs, the difference between the- value
ixT the common expedation, to perfonsat the
mean age of all married per^s taken toge-^
iber as . they exii^ in the world, and to pe r-
^6 at that age, which is to be deemed their
mean age when they marry.

Thus ; let 3 3 for the man, and 25 fot the
wonial>» be the mean ages of all that marry
anntiatly. Let alfo 48 be the mean age of
i\\ ^e married men in the world, and 4a of

married

44 * ^ifiiom^iMcermng ^ ;;

married women /Tir^*— N«wr, he diat will
calculate for tbefea^s, in the manner dt^
re£bed in <2[ucft, IV;. Will find, that Jthe. value
in;afti2flfa/\^i9ym^ff/j iiiiriiig marriage, end be-*
giofitng. immediately, of the expedation of
an ^asai^ty of zqL. per. annum by aperfon
^jLyearS'of age,, after a life whofe age is 33^
18 /..6.6i|..r^And that.t/> 8^04, is the value of
the faiue. expedlatioo^ the ages being 48 and

The forjDner, theitTorc* i$ the payment for
perpetuity from every: member of; the cfta-
bH(hment ; and the. v^lue of ih», differfnee be*
tween it and the Ifittttr, or of /; 1.4 ,p^r am*
payable during two joint Jives, whofe ages
are .40. and 48, that/is, /. i4f2, is the fine ne->
cefiary to be levied on every married, member
at the beginning of the.eftabliihment {bj.

It .would be eafy <ot extend the benefit of
fucb an • eftabliihmedt, foi fiu* as. to provide
i.QQ A for the children of members, .provided

(a). I mi^ft beg leave to refer to note (F) In th^ Apr
pei\dix, for an explanation of what I mean oy the mean
ages of married men ^nd women, and alfo for a confir«
matioii of the anfwer 1 have given to tbis.Queftion* :

*'(}^) 9in aimuity for ever, the firft payment ef which
b id:b)s made immediate^, is worth 26 jeearspurch^c^
intereft being at ^per cent. L 14.2 therefore^ rs equiva-
lenf in value to 0.55 /. or i is. per annum^ for even Ad&
this xk'h 6.64, and it will appear, that /. 7.19 pet ammm^
bdgMning Immediately, ia the anfwer to this.Qiieftioo,
fuppoiipg^thjc value of the fae to be provided for in (he
perpetual aunujil payments.

they

Reverfimary Afmuities^ &c. - 45

they* leave no widows ; and the neccffary ad-
dition oh this ac\:ourit ' to the perpetual an«
nual payments^ can fcarcely, in the cirtum-
ilances this quelftion fappofes, be txiuch mort
than about 1 5 x. payable during life, and ex-
cluding from all benefit fuch as happen to
be widowers at * the commencement of the
eflabliihm6nt> and d6 not afterwards marry.

« I '

Ify in' fuch an edablifhment^ all perfbns
of a particular denomination, whether mar-
ried men, widowers, 6V Satchelors, are fub-
jed!ed alike to the taxes 4nd fines ; they
oujght to be as much lefsy as the whole num-*
bCr of perfons fubjei5« to them, \% greater
th*ln the number of hiarfiages conftaiitly
ixifting. ; ' .

In carrying thefc fchemes into exeicution^
there cannot be a more eafy, oV eqajtabld
way of raifing the n^ceflary fines, min.by
providing, that none (hill be entitled to any
cxpefliation for a few of the firft yearsv Thus^
an eftablifhment, entitling widows fo 20/.
per annum for life, and confiftiiig* of 66^
married members, and 344 mrniarried, al-
ways kept up at an average, ought to begin
with a capital of /. t^.a multiplied by 667,
or 947 1 1, befides one payment in hand of
the conftant annual payments. That U# (the
proper. annual payment of every memb($r be-
ing in this cafe iV/r> multiplied l^ /. 6.64,
or/. 4.38) it ought to begin with a capital
* ' 3 of

4$ ' ^Jifom^onfirning

oii^^ql. over ai}d above th? pajtiifiit ql*
A 4.38, at the end of every year fox pvpr af-
terward? (tf),— The e^cpltjjfio.n of all jd^firft
izieml3ers from any beiie0t». uol^fs they fur^
vive tlje firft twQ ycajp, or live to make thr£i
P^yiQentSf vt^ould rajfe thi$ capital nearly*
Aad facb an cxclufion for tktee or four years^
would lie an advantage fo confiderabk^ chat
it would probably give fecurity and lability
to tbefohemc for all fubre<]^uent time.

In thefe obfervatJQn.s» I have bad in view^
feveral fchemes of the. kind defpribed in it^
which are now a<£lually eftablifhed in this^
kingdom i but more particularly, one heguij
among the London and Middle/ex cler^, an4
another v^hich is eftablKhed by ad of par-
liament »mpng the clergy in Scotland iot
both vvhlchji I fhall hftve occaiion in the next
chapter to take further nptice.

I have chofen to calculate here only from
pr. Matlefh Tabje, pr Mxp De Mokiris by^
foth^i grounded upodQ it^ beucaufe the LfOndpn
Table is^. by no means^ adapted to the cafei^
ip vi^W,

It 'fljouW be further femembcredj tTiat
wh^ jihp nje^n ages, jit which marriages
commenci?, .are fuppo^4 to be 33 and 25,

(^) Ojr, fuppofing the value of 94717. (the fine) pro-
vMed *ft)f in tne annual payments, it ought to receive
eveiy 7cilr,vai ifae t^kmivg of Ihe ycflr, )» «9t|tribotiw

* all

•il:£rcillttd al)d thki) ajarq^ges are j|icli|dkd;
and that it is to .be ex{>e^ed, that almoft. ^l
thefe marriages will begin after thefe ages %
and likewife^ that* a* eooiidenable proportion
of the firft marriages will begin a much lon-
ger time after thefe mean ages, than any of
the other firft marriages will begin before
tiiem. — ^prbba'blyy therefore, thefe mean agtt
ihould not \k taken younger. One or two
years, however, more or lefs, in every fup-'
portion I have made, will make no diOT*
rence -of any confequence«

Qjl S S T I O M XIV#

^< A perfon of a giv^en a|;e has' an eibce ^*
^ pending on fhe con^uance of his life fqr
^ a given term. What oii^t'he «o gifcifor

haviiig it affured to hi£& for that term V* >

4M

Answek.

. From the value of an annuity jpertain fiv
the given term, found by Table II, fub-
trad: the value of the life for the given terin>
^bimfi by Qgeft. VL and referve the rem^ini-
4er4-*-MultipIy the value of i /. due at U)p
cxnd of the given term, (found by If'able I.)
by the perpetuity^ and alfo by the pro6abfIiff^
tnat the given lUe 0x41 f^i).in the giytn tcxw^.
The proauSl added to the refervedxtarnxx^p
and ^t/um multiplied by the given annuity^

vili

4? ^efthns concerning

ivlll be ^the required value of the afiurance

in one prcfent pajment fdj. -

• * ...

' Ex AMP LE* .

. An eflate or annuity of lo I. for e^er, will
be loft to the heirs of a perfoh no^ 34,
ihould his life fail in 1 1 years. What ought
^e to . give for the ajfurdnce of it for this
term ?— That is ; What is the prefcnt value
of fuch an annuity to be entered upon at the
failure of fuch a life/ fhould that nappen ii^
1 1 years ? - ' *

The value* of the Kfe of a perfon whofc
age is 34 for 11. yesurs^ is, . by Queft* VL
^reckoning interefjb at 4 per cent, and calcu-
lating from !Pr* Halky's Table of Obfej va*
tions) 7.761 whiqlii.fub traded from 8.760,
(the value of an annuity certain for 1 1 years)
leaves i L the remainder .to be referved.'

The value of i /. to be received at the end
of 1 1 years, rs, 6.6496, by Table L The pro--
bability that the life of a perfon/ aged 3^,
ihall fail in 1 1 years, is, by Dr. Haiieyy Ta^
Tile, Tw; and in the perpetuity is 25. Thc^
nun^berSj multiplied bygone another^ and t
added *o 'the proUuft, make 4.34, Which,
multiplied by ro, (the^given annuity) givels
7.'4J.4, the rcquirtd^^altie in ar fingle ptcfcrit
'payi^ent;- . - '

• , * • * *

'^^ fa) See the demonft ration in note (G) Appendix.

/•434»

Reverjhnify Annuities, &c* 49

7.43.4, dmde^ by 1.04, gives* 7* 4! -•i^, Ac
true value/ by ^chc^ium to Quefti X. of the
aifarance of an equivalent Jum, or of 250A for
1 1 years on the givtn life.

A^aiQ« 41 «7, divided by 8*769 (the^alue
of the given lire for the given time with unity
adfled to it) givea 4*76, the fanote value in an**
una} piiymeats beginning immediately, for
II yews i^a)^ ful^jed to failure liquid the
life fail.

S C H O L I i; M«

» _

Iii t fimilar way may the price of sffuraft-t
cefe on arty two joint lives, or the longeft of
tT^ fives for any given icrmrs, be calculated t
the rule being: ^s follows :

•* From the value of arr aiintrrty certain
for the given term^ iubtradt the valae of
the joint live^, of the longcft of the two
lives for the given term^ found by Scho*
Ifum to Qucft. VI. and referve the remain*
«^ der.— -Mtikip^y the Value of i /• to be re-
** ecivcd at the end of the given term by the
«* 'pef petuity, and^ alfo by the probability
*' that tht Joint lives, or the /onge/i of the tnvo
*• Z/*^/, (hall fail within the given term. This
prodiKa: added to the referved remainder ^
and ^tfum multiplied by the annuity to be

€M
4€

_ • »

(a) The lad paytn^ent to be made at tbe end of the
nth year s or 12 payments in all.

•* aflured.

50 f^ftims CMfsrning

*i afTurcd, vfill be the value of the afforaacc
'^ in a iiDgle prefent paymcdu"

£ X A M £ I. £« :

^' What is the value of iq /. per annum^ to
** be entered upon, Should either of two
•• perfons, one 40 arid the other 30 years of
** age, die in ten years, reckoning intcreft
** at 4 per cent, and calculating from Dr.
" Halley's Table."

The value of two joint lives at thefe ago^
for loyears, (found by IScbo/him to Queft,Vty
is 6.51; which, fubtradted fromS.iii, (die
value of an annuity certain for 10 3rear8, at
4 per cent.) leaves 1,60, the reoiainder to be
re/erveJ.

The value of i A to be received at the end
of 10 years, is, .6755, by Table !•

The probability, that the lives of one or
other of two perfbns, aged 30 and 40, (hall
£ul in 10 years, is, 44t by Table III. (a).
And the perpetuity 25. Thefe numbers,
multiplied by one another, and i*6o added
to the produd, make 748, which, multiplied

(a) The probability taken from the Table, that a per*
fon aged 30, (hall live 10 years, is, 44^^. That a per(bn,
aged 40, (hall live 10. years, is, |4*^. That they (hall
ioth li^e 10 years, is, |^, multiplied by -J^f, or-J.*«.
That thev (hall not both live 10 years, or that om oi'omr
of them mall die in this time, is, ^44> fubtraded from
unity, or ^f-. See note p. 23*

by

ojr lo^ (the givfil aiinai^) gives L 74.89 the
liiifwer in a.fingie prefent payment.
, L 74*8^ divided by 1 1049 gives 1. 7 1 .929 tho
Value« of the afiiirahce of an equivalent fum %
or.of 250/.-^/. 71.92, divided by 7.51, (the
value of the two joint lives for 10 years witn
4inity added) gives 9«57> the value of the
fame fum in andual payments. beginriing im-^
mediately, for 10 years, fubjedt to failure
ifhould the jotiit lives fail»

EXAMPtE 11;

» . . , .

I •* What is the value of i o /. per ann. to be

^^. entered Updn, ihould two perfbns, one 30^

f' and the otfae]:40$ 6btb6ici that is^ ihouid

'' the kngefi of the two lives fail in 10 years;

reckoning intereft at j^per^emt: and caU

culating frorii Dr. HaOef's Table ?"

The value of the longefi of the two live^

for ID years, (that is, the value of the joint

lives for 10 years, fubtraded from the funl

of the {a) values, of the fingle lives for j d

: years) is^ 7.91 \ which, fobtraifted from 8. 1 1 1^

. the value of an^annuity certain for 10 years,

leaves .20 the remainder to be referved.— -^

The value of i /. to be received at the end

fef Id years, is, •6755. The probability that

the lives of twd perfons; aged 30 and 4a,

fliall fail in 10 years, is, by Table II li -AV*

. (u) Sec Schotiiiin (0 Queft, VX;

«

1

€€

multiplied by ^^ or t ilU r i osmI the per*
petuity 25* Thcfe numbers, multiplied bjr
one another, and «2o added ta the produdt,
inake •740, which, multiplied by 10, (the
g^v^n annuity) gives 7*4, the anfwer in a fin«
gle payment.

7.4, divided by 1.04, give^ 7.1 1» the va-
lue of the afiurance of i^oL

Remark L

The values of fingle lives for given terais^
when thefe terms are lefs than ten yearsf
muA* in aoTwering thcfe Qneftions^ and alio
in anfwering the following Qjieftions, be
found true to at kaft 2 or 1 places of deci-^
mals. Bttt they cannot be lound to this ex^
a&neis by any Tables that are extant ; and,
therefore, they muft be calculated in the Soh*
lowing manner :

^^ Multiply the probahili^j taken out oi
^^ the Table of Ob&rvatioiis^ that the Ufe
^f (ball exift i> 2^ 3, &c. years, by the value
^.* of 1 /• due at the end of 1, 2, 3, &c. yeaisj
\* and the fum of the pcodu^ will be the
'^ value of the life for i> 2, 3^ &c. years«"

. For Elample. The probability, that a
perfon whofe age is 34, £haU Uve a year, is,;
by Dr. Halky'% Table^ ^^ The probabai-^
ty, at the fame age, of living 2 years, is, ^tt >
3 years, t54.-^t^ multiplied by .9615, (the

value^

Jleverjionary Annuitiesy (xx:^ . g^

value, by Table I. of i /. due at the end of a
year, intercft being at 4 per cent.) is, .942 ;
or the value of the life for one year,— Jrrf
multiplied by .9245, (the value of i /. due at
the end of nt years) is^ .89 1 . And this a^ded
to the former produdl, gives 1.833; ^^ *^
value of the life for 2 years. — Hi multipli^

cby .8890, (the value of i /. due at the end cf

'3 y^f^) is^ r<S4f; and. this produd, addcfi
tq 1,833, niakes 2.674, or thcvftlue of the

ygiven life fqr 3 year^.

;. When the tfrm exceeds iq years, the rtflie

in Queft* VI* will give thefe values with C^
iicient exadnefs ;. and it would dp the fan;^
411 all cafes, were the values of livos given
true to 3 or 4 places of decln^s, andv.^

i^ri£t agreement to the Tabtes of Obfer?a|i(^ii
ufed, ;

The renaark now made is to be extended

.to the values of JoiMt lives for giveir ternaf.
For thefe values, like thofe of ^ngle lives,
cannot be foi^d in klvimg thefe QueftioOs
with fufficient accuracy, when the terms arp
fmall, by any method, except the tedious
one, of multiplying the probability that the
2 lives ihall iafi continue 1, 2, 3, &c. years,
hy the value of i /. due at the endr of 7, a,

.3^ &;c. yearsi and taking the fum of the pror
du£ks in the manner juft described.

E 3 REMAltK

j»4 ^eJRcns corwernmg.

•Remark IL .

If the annuity i§ to be entered upon, m
cafe of the faikire within a given time o^
any life or lives, at tht end of that, titpe i and
not at the en^ of the year in which tf^e failure,
may happen ; itis prefent value v/ill be the pro-
duct arifing from the continual multipljcatioa
4]^y one another of the perpetuity incfeafed
♦l^' unity ^th^ value of i '/.' dup at* the end ot
l!ne ^iv^h time; the annuity ; and the proba-
bility that the life, or lives', fliall fail within
fhd given time. And care fhould be taken
ubt to' cbnrbund thefe two ibfts or Queftions
with one another.— Thus ; the value in one
payment of i o A per anti. to be entered upon
eleven years hence, in cafe a perfon aged y^
ihould not live fo long, is -16, (the perpetuity
increafed by unity, intereft being ztj^per cent.)
multiplied by .6496, andbyfo/. and. alfo
by ttt; or 34.8.-^This vake, divided by
1.04, is, ^3.5, the value of an equivalent
fum, or of 250/. to be obtained pn the fam(;
conditions, . ^ : / ::. *

The vakie ctf the ajkrance. of any annuttv
on the whole continuance oF any fingle life
is, by Queft. X. the exce^ of the perpetuity
iibbve the value of the life, multiplied by the
annuity. And in fike manner; the valae pf
the ajfurance of any annuity on the whole
continuance of any two joint lives, or the
hngeji of two lives, is t^c excefs of the per^

petuity

Revirfiohdry Annuities, &c, 55

fetutty above the value of the joint lives, or
of the Ipngeft of two lives, multiplied by the
annufty. This is very obvious \ but no ge-
neral method has been yet explained of find-
ing the values of ajfurances on lives and fur-,
vivorlhips for terms of years lefs than the
whole continuance of the lives. For thi« rea-
fbn; ;I liave been here more explicit than I
Should otherwife have been; and, as fuchaf*-
furances are now -much praftifed, and may
be very ufeful if their values are, rightly dei^
termined, I have thought proper to add the
two following Qucftions, which, when join-
ed to (^eftion XL and Mr. Sinifforf^ jjd
Problem given in the note, p. 39, will, I be^.
Ifcve, cxhauft this fubjedt.as far as two Hvm
can be cbncei-ned.

^ * k

Que s t I o n XV.

** B, expedlant, will lofe a given fum,
** .flipuld he furvive A^ within a given time^
♦^ What ought he to p?y fpr thp (tj^urance of
f« it ?•' — In other wortjs ; " WVt P^ght he
** to pay for a given fum to be received at
<' the. death of A, fliould he happ?P to fur-^
<' vive him within a given time V*

A N rw E Ri

Divide the fum of the decrements of life
in the Table of Obfervations from the age
pf A> for the given time, by the given time 1
s^nd, by the quotient, dvd^t the number of

£ 4 the

S6 Stgeftions concif^mng ;

the living in the Table atthpage Qf.Aj^.Aod
again, foy this /econd qujoti^nt (a), dir^e-t^
given funit referving the ti^n-d quotjcftt,,.

Find tbe valaeof an annuity pn.thejUfe
of B^ for the given time. To thi$ yajjif ^^^
the quotient^ that will ajrifc froijp dividing t^e
value of an annuity certain, for i^p gi.yeii
tiniev by twice the conOiement of tjbe Jiff of
^ ; . and the fumf multiplied by the rfferv€4
fuafim^f will be the required value in ^ fing|p

prtfc^^ (^)i payment. / /; . '

if *

" Example, • ' " ,' . •''

Xfft thue Tablqof Obferv^tion^ be Mr. Sfmpr
/o^Ss for J^nd^n^ or Ta.ble. YIJI . L^et the t^
pf iptgreft be- 3 /^r (Ttfiwf. V .A, fevcn ysear^^j^
age. B, 30. The giverj,,?fpw;. 14 Jt^i^^i
The given fum 100 /.—The fum of the de-*
crements^ in T^We;V|IJ*/or ^4 years from the

vcn 18 430i Which, dmded by^.2j"and^i9o A
divided t>y the ^quotient, gives h'r,2.i, .the
quotient to be r^erv^d.^ ' * ^ ' ';* 7 ; ''

(a) When the' age of A is under 6b, iiiid t;jWc tertn fo
large as to exceed Uhe difib-dnce between- ik )EiAd 76, h
will be beft when the Lonaon Table is ufed, to divide
the given fum, not .by thafe<ond, quotient here menti-
oned, but by the (ompliment of the life of» A,.t3kie;i out
ofTablclX. ^ " ^

(h) See the demonftration of tnis rule, and alfo gf the
rule that will be given for fdViitg the ncxt'*Qtrellion, in
tb^Appendix^ note (U)^

; : ^ The

; The value of ifk ee«itity/er 14 ye«r$ on
the life of B, a by <iu4{ft. VI, 9.5.— The
value ef an annuify ccit«is f&r f 4 ye^rs^ i^
by Table II. 11.2961 which* divtc)^ bjr
ift4i4> (twip^i.^the fpmpkmwt of the life of B,
%.T»ble IX (*)» giv^s . I a,, which, ad4«J to
.9^tf-ig\ve8 9,^:^; and thi$ . a^a .mjdti|p^ieil
Sy j.2i[t the r^rv^d gMtifnfx^^^ u»64,
tkf^frefent Taluc jia ^w pay meol ot 1 ob.A pay-
able at the death of A ag^d 37* to B ^gecl
^p, (bould A . die and leave B the fvrvivor
,f)urithin 14 year^*

r ,The prefept vnk^e for J 4 years of two joint
Ijiye^Sj one 7 and the other - '30 years of age^
jgayhff. found,. hy the help, of TMc XU^mA
-Ihe rqk in.th^y&cAoUum m Q^.YL te be
mf^sky.g yiearfc ip»Jrch4fe 1 and, 7.11,64 dfe.
si^A hy th^ .value with unity added, ot by
16, jgives t%i^4» the foregoing ValUe in ^;^-
nual payments during the joint lives for 14
yearsy the Jirft .paytnefit tb be made imme-
diately, and the laji payment at the end of

14 years, (hould the joint lives not fail* •

Scholium.'

• » • »

It defervcs particularly 'to be remembered,
that in this method likcwife may oe calcur
latcd, what fums oi^ght to be* paiH oa anv
furvivorfhi^, within a given tjjmib, of one liie

' ■ «

(a) This Table gives the expirations oqly, tut it ftould
Vt irnflehibered, thftt. twice the expe£fati9n is iJvajrs the
milfhnfnt of a Uie. See note, p. 37.

beyond

I •

4>cy'di<d', atiothcr, in cohfideration of any gj-

^eli funj noW 4dvaniefe3.-^Thc fi>llowing Ex»^

iimple of this is ^*^^t w)ikh has ofFeried Itf-

felf in pradiceJ - ^ . * i

<< A peribn^ aged 30^ hdk in expe6tiitk}{|

;*' an eftate which i€ to come to-hirt> pro^

** vjided he ftirvives^ a -minor ^ aged 7, bdforic.

t^* bc^ fe oyt*bf his minority 5 that is, -pro!^

*^f yide4 he ftK)nld be himfelf living at the

^^ time of the minor's death, fhould that hap«

^\ pen before he ie 21.- — In thefe circuthr

*^ fiances, he wants to borrow 1 qoo /. on life

** eocpeSlation. What reverfion out of the

rf^ eftate depending on fuch k furvivorfhip, i^

f * a proper equivalent for this Aim noW\.id^

*< vanced, intereib being npkoned at 3 'f&

^^ cent, and: th€ probabilities of life beiiv^

f^ fuppofed^h^ f^me with thofe in Mr. Simt^

f? Jpn'% Table oi London Qbffefvatlons ?t.

Answer,

It appears from what has been juft deter-*
mined, that for /. 11.64 now advanced, the
proper equivalent in fuch circumflances, is,
xoo/. to be paid^ in cafe the furvivorfhip
fhould take place ; or, by the correStion in
page 34, as much of the eflate as 100/.
w3l buy at 3 per cent, fuppofing the lirft rent
to be received immediately ; (that is, fup*
pofing the eflate worth 34*33 years purchafe.)
or A 2.912 per annum.. — By the rule of pro-i*
portion^ therefore^ for looo/. the prqpi&r

cqui-

Revtrfiwwy AnnukieSf flee. 5^ ^

ccpihrticnt'Mrill be 8591 /. in xnoiiey, or 250 1^
par annum out of ibe cftatp«

■ I ^

Qj; R 8 T I Q-M'- XVI.

<« looA W^ll be loft to B's heirs, fliould ho
i^ happen tq die after A, witiin a 'given time.
f* What is the price of the ajlurancex>f it ?-t^
f* That is: What is the prefent value of
f* looA payable at'the death of B, provide4
ff his death ftiou)d happen ufttr i^% d^ithjj

A N:S W E R. . '

Divide the fum of the tlecrements of life
|« the Table of OBfervations from the age of
"B; fbr the given time, by the given time^
and by the qUottent'dKwiAt the number of the
living at the age of B; and agaib, by this
Jeeond .quotient {a)^ divide the given fum, rc-p
fcrving the third quotient •

Find the value of an annuity on the life A
for a rtumber of years, lefs by one year than
the given time, which fubtraft froni the va-
hie of ah annuity certain for the fame num-
ber of years. Multi^y the remainder by the
referoed quotient ^ and divide the produSt by
the amount of i /. for one year» and let this
|)e Tifecond rcferved quotient.

(a) Qr rather. If the Lindon TaUe is iHed, by the ccm^
pimeftt of the life of B/ when bit age ia under 60, and
the term exceed3^tbe i&ffertnci between it and 70.

Again*

/

<6o •'^^^^e/NMScoftc*^ifhj^ ^

. *Agaiii/' .Mult iply into one tn&thet Vtaijbjl
referved quotient; ami d^d valute of an an--
nuity certain for the given time ; and divide
the produ<3i by twice the complement of AV
life. Thi$ iafi qjfppf^ added to the fecond
referved quotient, wiU be t^e (wfi/per iq ^i.pre^-

lent iingie paymeiM;* ■ ; ; , »

\- »

.•,',, , . ; - E -x; A.M p t sr,.- /.,:

^ Let tKc ageof S be 401 Of A 30. The
fum 100 /. Rate of inter^ft 4 per^ oeHf^ The
given time 20 y^ars. The Table of Obfer-
vations, Mr. Simp/bn% op -Table VIII. — The
fum of the decremeatsr 0/ lifq, in thisT^le,
from tbe,age of 40 for ao jears^ i$ i a^^which,
divided by 20^ (the given tixsae) ^ives 6«38.-*-*->
The nymbex^x^f the Hv^^i^^t 40 is^ aa^^which^
divided by 6^36^ ^ives 35.S f-an^ 100/.. (tfae
^iven fun)) dividod by 35.8, givei a.79^ die
Jirfi quotient to be^f^^eryeij..
/ The value of an annuity for ^9^ yearf on
a life at 30 years of age, is 10^3 f whicb>
fubtradted from 23.1 34, (tjbe v4ue^o£ an aiv*
jiuity cerfein for i9,years, by Tab)^ II) anfl
the remainder multiplied by 2.799 gives 7.89.
This prod^dt divided by 1.049 (the amount
of I /. ;in qae year), gives 7.60 1 tbc Jfcan4
referved quotients

2.79 multiplied by 13.599 (the value' of an
annuity certain for 20 years) giv'es 37.916;
arid this ptoduSt divided by 94.4, (twice the

com-

ReverfimMy. Annuities ^ :Scc. 6 1 '

complement of A!s life by Table IX.) gitres
•40 J 9 whkh^ added . to 7.609 gives 8/. the
Anfwer ^ or, the value of 1 00 A payable at the
dmh of B» on the contingency of his furviv-*
iag A. aged 3O9 MAbofb ^ing in ao years*

It is plain^ that this is lil^wife the fum
that ought to be lent to B now^ On the ex-
pe£buion of 100 A at his deaths provided it
iboold happen 4ftef A's death in 20 years.

This rule gives the juft foluticm in all cafes^
except when Bi the eacpedant^ jis Hm ff^ungeji
of the twa lives, and at the fame time tho
tenn of yeai-s greater than the conoplement^
of A's life. Ip this particular cafe the foK
lowing rule mufl be uibd* , .

Find, by the preceding rule, the value of
the aiTurance of the given fum for a term of
years, equal to the complement of A's life,
and let this value be referved. Multiply by
one another the given fum ; the valm of i /•
to be received* at the end of a number of
years equal to the complement of A,'s life ;
ioid die value of an armnity certain for as'
many yea^s as the given term exceeds this^
complement. And the produSf^ divided by
the complement of B's life, an^ the quotient
added to the value referved^ will be tlie true
value ibught.

Example.

Let the age of B be 30; of A 40^ The
term 47 years ; and ^very thing elfi: as in

the

the laft Example. The complement of k'k
li&9 .is^ by Table IX^ 39*^; The value o£
I bo/, to be received at the de^th of B; if he
^mv6s A within 39 years, may be fdand
by the .preceding rule, to be /i i6;i5 3 the v«*
l«e to be rcfervcd.— ^The value of iV* to be
deceived at t^e end of 39 yeat^is, by TaU6
11^ a.i66. The valuie of an tnouity cerium
for 8 years^ (thfc exce& of the eiyen tersd
above the complement of the life of B by
Table IX.) id, 6.733.

And thefe two values multiplied by oiie
toother, and by 100/. give 145.83 5 which,-
divided by 47. 2i (the complement of the life
of B) and 16.15, added to the quotient; make
/i 19.23, the value fought;

k E M A R Ki

As alter finding the preferit value of aH
feiiate, or annuity, it is rieceflary to divUe
that value by the amoUnt of iL in one year^
in order to find the prefent value of a fum
equivalent to the anriuity ; fo, after finding the
value of a fum, it is heceflary to multiply that
value by the faid amount, in order to find
from it the value of an equivalent annuity.

In the firft- example, therefore, the value
of an eftate o^ 4/. per annum y would be A 8.32:
In the fecond Example, 20 /. And this isi
as it ought to be^ the value for the whole
duration of the lives, agreeably to the Pro-
blem in the note p. 37%

I In

Rmerfionary

kc.

H

hx folving this Qgeftion» care alio muft bd
taken not to ^get the Jirfi Remark under
die foregoing ,Que(tion.
* In the fame way with that in which die
rules* in the three laft Queflipns have beea'
difcovered^ it is poffible to find rules for cal-
culating the values of aJfuranceSf far given
/irrmr» on lives and furvivorihips, where three
cr mcrre liveis are concerned. ^ But this is of
lefs importance; and I chufe to leave to
others^tne further profecution of this fubje<9:*

CHAP.

• < 1^ •

• ■ • >

i H 3

• T

» »

CHAR tl

•' I

.//««f t« i^'^.fif^fgoing Chapter to th^.
Schemes tf the Societies in Gx&aXt
Britain, for makhtg Afiitait€e$ m^

Lives ' md ' Survivor jhipSy and, fof^
granting Annuities to Tf^idowty ami
to Perfons in old Age,

S^ E C T. I.

Of the London Annuity, and the Laudable
Societies for the Benefit tf Widows.

TH £ fcheme mentioned in Queft. VIIL .
is nearly that of the London Annuity
Society. The Laudable Society is alfo formed
on a iimilar plan. In both, the annual con-* .
tribution of cvtty member is five guineas^
payable half-yearly ; and for this a title is
given to an annuity of lol. to every widow
during widowhood, if the huiband, after ad^ ^
XtiifTion, lives one year according to the Jirji
fcheme ; or three years according to the {a)

(a) In this fociety a member who Kves but one year,
19 encitled to no more than an annuity of joA for hxs
widow ; if he lives two yearS) 15 L if he lives three yearly
20/. four years 25/. feven years, 30/. ten years, 35 A
thirceen years, 40 /•

5 fecondi

Of tU Ldndoh Anhuity, tSc. 6$

fitrndi of 30/. if thehufband Xvft%fevenJ^^x%i
according to both fchemes j ftod 40 A accord-^
ing to the Jirji fcheme^ if he lives 1 5 years,
or 13 years, according to the fecbnd.-^In
both fchemcs alfo, there is no odier pre«
iriium or fine required, than five guineas ex-
traordinary, at admifiioni from every fntfai*
ber wfaofe age does not exceed 45; . The
Laudabk Society admits none above 45, and
the London Annuity Society obliges everv
perfon between 45 and 55 to pay, at adlIli^-
fion, five guineas extraordinary, for every
year that he is tarried of 45.

Thefe are the main particulars in theA
fcfaemes ; and^ therefore, both of themi were
the annuities . to be enjoyed for lift, wouU
receive (fuppofing the members all onder
46 at admiffion, 4ihd of the fame ages with
dieir wives, and money at 4 ftr cmti) but
little more than tbree«fifths of the true value
of the annuities i or about one half, fuppo«
fing wives, one with another, 10 years younger
than their huibands ; as appears from Quef*
tion VUL

. It appears further in that Queftion, that,
fuppofing the annuities to be life annuities,
and men and their wives of equal ages, the
expedtation to which an annual payment of
five guineas beginning. immediately, entitles,
is nearly 14/. it the contributor lives a year,
and 20 /• if he lives fcven years (a), taking

i^) Tbc fame annual payment will, on the fame Aip*
^ lUons, entitle to 14/. if a member fives a year, anci i8/.
rrhc lives tbrei years.

F the

<^ Of the LoDcbo AxSMotf

the medtttm- between the Lombn and, thk
ether Tables of Obfervstionfi.

z. k-is Hkefy^ that nuny per&ns will be verjp
vawilHiTg to< beltcve, that thefe fchemes ara
lb dofioieot as dbey have been now reprefent**
•d. I wilU ^Krefpre, endeaTOur to prara
liua in a way which» cfaa' lefs fbrifk^ i$ fvrffr4
cisntly deci6?e> and may be more Hhdy tfr
beinteliigibic to ^perfbns unfldSled in mathe^
maaied calculation .-«»^ (hall here coafine my^
fetfilD tbft llpheme^ the LMubn jitmuky So^
ciety. The difieicncet between it aiw the
fididner pf the JLaudaiie Society are inconfi*-
defable»:ahd what ftijdl-fae &id gf liie one wtfl
be JuUy , appUcaUr to the t>then
*: iboconding' to^this fcheme^ aa it hasbeeit
yoAAc&xibtil^ ^ that Irae j$ jais in th^
iadet3rii!iU^b^ entitled- tor auMiitiea . of '4oJ«
fir atmum &xt thm widomcs. SiipfMafe tilie
whole fociety^ at admiffion, ta.be men of 40
years of age^ taiaai one \ttiib aoother. ' A
peif(}in of. this age has ai\ earea chance of /w«
ing 23 years ; and he has an even .chance of
Ctmtinuing with a wife of.the/iusie ^y (diat
is» of Qontimiing in the fociety) 13 ycMsl
and k [fl). Ifot much lefs», thdrefiDre,. tfaaa

{a) This IS thecxad truth according to Mn ThMih-
vr/s h)^bthe(tg, aiid the Norwich Table. But accord
ing to Dr. Helliys and. the N^rihampun Table, a pM
40 years gf age has an even chance of livi;ig^no mole
ihan 22 years, and of joint continuance with a Wife of the

feme

and Lftu(kble S»&fMH "ICt. 6f

kaH the members >will continue in the ibcin^
ty IS years; uri» confiiquentlyi riot much
le& than half the widowt that will 'Cotne
upon, the ibciety nviU be annuitantt of.< 40 L
pir annum^ Theie widevrs, howcwr^ : being
elder than the reft; when they cbmosenCe an«
nuitaotSy will continueron the fociety a ifaorler
time; aod» thecefece^the number eenftantl^
in li£r tqgediel'j to iddch they, will in a
coorfe of yeads na*ea&» .will be pro|)ortion>*
ably iinaUer. ¥\xi\kn% ewcry thing as £uraur^
ably aa poflible^ kt uafeppofe^ thait out of
ao: anauhanta conftantly on the ibcietyt Jhe
wiU he aanuitants of 40 /. jSx of 30 A and
nim ofao/. . Tn 20. annuitants then the £0^
ciety will pay 560 L pen onmiMf or the 20th
part of this inn), that is 28/. to ^^annut'i*
t^nt.at an average* Blat fuch ah .ammity for
a life at 4O9 after another equal life» provide*
ed.both furvive one year^ is wordt (by Queft.
i[lh p. Z4O in ^ fingle prefent payment^ 85 L
nearly, ^ocofding to the Ltrndortf and ^ the
Tables of Obfenrations, intereft being all
along (appofed at ^per cent^

It cannot .appear^ .improbable to any one^
ikott this (honld be the true value of fuch a
reverlion. It is not probable, that there is
any fituation in whicn the decrements of life

ftme age, ig years.-*Forty muft be more than the mean
age of the members of the fociety at addiiffion, and on
this' acccont the number of annuitants of 40/. muft be
proportionably greater. The mean age^ therefore, has
l(eeqi taken very moderately.

F 2 are

69^ Of the London Annuity .

arefiich as can make it a tenth part mora or
lefs.-»<'8'5/. in prefcnt payment is the fanrer
with 3 /• 87. per annum for ever««~Bnt is an
annual payment of five guineas, which muft
ceaib as ibon as either of two lives each.
40 fails, equal in value tafuch a perpetuity?
£ very one muil (ee^ that ^re is a ^reat dif-^
ference.-— A fet of tiiarmges between per«
fons all.40» will, according to the probabili-
ties of life in Dr. IifiUey'% Table, hft, one
with another, 1 5 years {a) ; and an annual
payment beginning immediately, during the
joint continuance of two perfons of this age;
is worth I b years purchafc {6). The com*
parifon then, in the prefent cafe, is between
3 /. 8 J-, fer arvtum for ever, and five guineas
per annum for 1 5 years i or between an an-
nuity of 3/. 8^. worth 25 years purchafc^-

(tf ) See the beginning of Eflay I.

\b) The value of fuch an annual payment, by TabUi
XI, or the Lmdw Obfervations, is 9.x ; and jo.8> by Mr.
Di A4lnvr/s byporhefis»-r-I biCve not taken into this ac-
count the five guineas yfti/ paid at admiHibn, becaufe it l9
obvioufly of too little confequence to make any confide*
rable difference. The allowances I have made in favour'
of thefe fchemes are more than equivalent to it. In par*
ticular ; it ibould be remembeited, that the calCulatioDS
fuppofe, that the payuKiits required by thefe fchemes^ are
yearly payments beginning immediately i (fee p« 28) and
that, the firft payment of the annuity is not to be made
'till the end of the year in which the hufband (hall die^
and alfo, that the annuity is to be paid yearly, and no-^
thing to be due for any part of the year, in which the an*'
Quitant fhall happen to die. .

and

and Laudable Societies, &c« 69

vA an annuity of five guineas worth only 10
years purchafe. ^

But to throw this fubjcft into another Aight.

Let 4he number to which the fociety is
kept up be fuppofed to be 200. . It. has been
dempnftrated ia.(^eft..ll» that at kail half
this number of widows will In time come .to
be conftantly on the fociety ; and it has alfo
been' juA' now. ihewn» that the medium of
annuities^ payable to them^ will be.s^t IcAil
28/. After a courfe.of year&i» then, the fo-
ciety will have a conflant exp^nce to b^ of
sSoo/. fer annum,r^Bvi\, what will be its
income l^^ln order to . dttermlne thii^# we
muft ccnfider,. tha^ !there are t wo., foutreft
ffbm . whence Its . income will be derived.
Firft>> the annual payments of the m^mba'Sv,
And, fecondly, the niibney accumulated, . or
the carnal rai&d during the time the mum*
her ot annuitantSLii Cdmipg to a maximum ^-'-^
The firft of thcfe fources affords 1 000 gui-
9eas^ or 1 650 /• fkr annum. This wants
J 750 A of inc annual expencc juft menti-
.onedi and, therefor?, jh order that the in-
come of the fociety may be equal to the bur^
den upon it, when the* annuitants come to d*
ffoximumj there muf^ be 'a fund raifcd in the
mean time equal to 43^7^0 A or to aq eflate
in perpetuity of 1^50/^ per annum. ^^h\xt
1 050/. per annum bk^nmng immediatdy,
and forborn 25 yesirfit And improved, with-
out lofs or delay^ all that time at 4 per -cent.
-» F 3^^ com-

yo . Of the Lotkdon Annuity

contpound intereft^ will l)at j tifl r^£t/ fEdi
a capital {a). There is, therefore, tlwfalleft
prop£, that the fchedie I /am donfidering
is extremely defioient* The trutti:is; rhat
fcarcdy a /i6/Vi/ X3f {bdi 'a capital bould W
faiied^ as will appeir.frcnq^ the foUowlng ob^
fervations; . 'v ^

Out of zoo perfoos, all 40 years. x^f age/
mopi than ^Te, according to the Lofidan Ta-^
ble of Ohfervations, and not (o xmriyhySn
JHbiiST^s vTable, fMj he expedted Wdfieinia
year; * Siippofe tbert rfl ve-to be. Ac rftaLVmnl*
btf o£ members that wiU die th&4frflrr.yoar
ef the fociety. In fubfe(|uent yearr the t:ol«*
Jedif?e body 6£ mend^err will be ccMktxniiaUy^
growiAg olde#; and;^ldKref6re, the |3rQpor4
rioa^ctf them tha^-witt di^eirery year, .iviH
br contihualiy imite^iing) 'iitt it\gets to is

mttocumm. \ will; however, fuppofe,: thati

•\ • , » » «

fa) Ev^QueftiQUQf thi^^kind Jjia? bte. ea% (oIjr#
in the iolicMnring manner. ^Iif Tal)le I> liod the vaLqe^f
I il payable at the end of any number of years ; and any
given annuity divided by t}iat^ Value, wtll be the ahmi?pf
ۥ which tlle'given annuity wiU in that number. .pf ^]reiu*9'
iAcreafe»-n-Tbus $ the pr^teiu Vfilue.pf i /. pyab.li; at ,thf^
end of 2 J yearj, is •375i,,rQckdning iatcretik ^* ^ter
cent, and 1050/. per annum ttivUedVy **yfiu ^^
2,800/. /tfr annum^ the jAQQe^ed atmuky ariSiig 1:00:
JO^oL pirann. In the &^<i ^manlief i(;mau ^foun^,:
that the fame annuity, forWi^ii; years, wilnnc^-eale to
1610/. per 07iirfr)9i.— But a 'Oiore' particnlar accounted
this will be given in the ruks imAtxibd Co the l^bteiat
the end of this work *;.'. * • c Ij .>

5. - ^"^^'^S

end Laiidiibk Sffcutki;. ^. 'jiV

^■dmg the ficft.so ^arr nd nam An tfar

Qflnher jiift ^deified will diei^Mry^ydik' f andr
thai^ cottfequisiiify, no nmrarthM^V^ «9Rlb«^i)
iinll' come avery ^year on &o-{bciety. * 7Bb
ages, of all tbcife;. widows^ wlidn ttn^* ctinr^
mcnco widowhood j( wiJl> it iti CHdont^^'faty
bocwceh 40/ and 6o. One mth moriuv
tiicnv they mnirb^ coofidered as hating cma J
fiicaoed^widowhyood ^ 50 years-of.age; Noivy
five widows ieflt every ydar at this slge, trill^
in ao years, incroaii^ to 4^ coiiftaii4y in. Ufo
together, according to the expedatsons dl
lite in Tables III, IV, and V^ und, ift 2d
years, .to 70 (i^). Soppofe theiraejkiitibea
alinie together at the end of aO'^yrardto'bo
only 6a, the greater part of thefcwill be
soauitants of 30/. and 40 A pet^ anm and thd
tefb ao7. Were the former only equ^ to
^.latter, the medium of annaitlw paytlUd
to. them wou]4 ^^ceed 25/. S^p^ofethon

»»

(a) Every ^alci*l?tion. of. thit kiqd* iatf^ftfy made bf
the rule i(i note (A) lA the Appendix^ — ^I knvj^ put th^
number living together at the end of 26 yebln at^^i, not
oM/tftat the reader HbiUr 'fee better faKlfted' thift ( ^tve
}pcpt low enough^ bttAUo to make f n sillowniccilivr iticH
widows as will be left by thofe members w)»o die withiji
a ytzt after admiilion,' ana wAo, therefore, according t^
Ibefe fchcnftes, Wift be*i»ikit!cd to tMr^itAufties. 'ffch
allowance is 1 00*10^ t.tfir^srfirerJtiio &ril yesu* of Ite
fcheme, \i will f\ot Xapt^R above oAce- ih 4 ^r 5 f carS|
Ibat tfie death, oi^*a mtQ(iber will ^c^fo circumliance<il,
fiippoflog the'j^rdteibility that a ma A*' ^t 40 Will live a
jr^r, ta be, d$ all but thtlAndm TttMei aiake it, 56

F 4 thit

yt Of tie Londari Anwiltjr ;

lUs nMbuan to bo no-nofltrtHftir z6h isid x^
uriU ioUow^ that, at the end bf 20 yeam^:
jtfae iociety will htre ao aimual peotto|ui3h
of 26/. multiplied by 6a, or 1612/.. and, ifi'
^CA able to bear fpch an expcnce^ it muft^:
in tbc infiermadiate time, have acquired an:
tncreaik of. income equal to thcjdifiereace
between 1050/. and i6izlfieran^. : Tfaaitr
ifi I it miift, iiKith ita favinga, huta aoeumvH
lated a ftock. equal to 562 A fer akki andr
imorth 14,05a/. But at, daring this timcv
there will be a number of flimuitaots^con'^
itantly Jncreaiing, to whom y eorfy payments
muft be made, the favings. of the focietjr
cannot .certainly be ooe.half of what tfaejR
would 'have been. had it be^n aU the tiiqo
free from all. burdens. Suq^pofe thai:; the
ftock produced by thefe favings, < to bceqiial
to the ilock that would ari&fcom an.iocpam
diio^oL per ann. beginninjg immedsaielyv
and improved pcrfeftly at 4 per cent, com-
pound intereft, for half th6 time I have
|ncnj|pnqdV Of for 10 yeai-Sji withoiit bdngj
fubjc^ (n^.a^y (:hecks or d^jidtionse fuch ao
income thus improved, woold^ in 10 yearsy
produce an additional income of 560 /• per
aflnurn^ or a capital of ^4,009/. — rAccordmg
to theie Qbfervations, therefore, the annual
income of the fociety at -the end of 20 years,
and befprf a third part 6f the highefl anniii-
tants could come uppn it» woUld begii^ ito
fall ihort of its expences. Abput that time

then

end Lmidabk SxikiU^ bxu 73-

Uieii:k*woold'neccftnlf ron agMMinds and
long^ before tlie number xi anmiitini^ oould
riic taa iop» it would fpend.its whole ftock,
«d find hfelf under a necefiity of elthef
dofibHng die annual piytneht^ of its metii*
bersVor bf.redpcing the afniui tits one half/ '
"^ AH Ihav^ Aow faid is ixietjnt on the fiip-'
ppffficm^^rthe ifcdkj^^^b^^ with 200!
memberft\iit46 ^ears of age/ and i^ afrer^ards;
liixritbdtb tMt ntisnjl^er; by ad^mitting no iiiofe
neyr rtcmbdrttban^'^^Itt.jiift/ilpply the va-
eanc|el^ocr^fion<4 by d^ of old mfem*
bers^. i£ it if sdlowed ttf incireafe^ it niiay con^'
tittue a longer time. ^ Aiid^ for this reafon, i
ibfaii)tyf>]iat Wfuitt half tb^ ^eflftry

krf?W^ i?i«fn^ancnt, ipiy very well $ibfift^
aiid even proipef for 30 or .40 year^.-^^Tbps^
the Laudable Society^ was it to keep to its
pp^efotit oftmber-^ fi^emfoers, might pebbly:
£tel no'deficiencie»fbr 20 or 30 years to conie^
bat if it'fliould continpc to increafe at the rate
gi 70 or 8a every year, it would, at the. end
of that time, pofieia 4 balance fo much in h9
favour, jas might enable it to fupport itfelf for
20 Or 30 yeaf» qaorc {a^ But bankruptcy

» ' . would

.... ■• « . . .

(fl) What li» been before demdnftrated in Qiieft. Ill,'
ihould be bere recolleSed, tfia'tthehumberofannulcants
en firch a fodcty as this, miitt go on to incrcafc^for more
than 100 year^^ after acqoirihg its greateft number of
members.' ^ '

TYit. Laudable Society, I am Informed, te6k its nfe
from a calculation contained in a pamphlet entitled,- 7%^

Pof^

^uld cpnio at kA^ aiKk^itbithfc'iiiofe.iecri^
bit weight the tongenit^Jiad:hQfai-ddfori'qd« -:

a f • r •

1 The rule iaiS.£W(i«\!^«w/ft^
w« obliges. fiverorperfoA bj^wcwi 4p^agefc
of 4^5 and 55,, to^jpay at admiflipfi -^5. guineas-
«ftjr«orduiary,;r9r.py^iy,Y6ij: tiiat;jp <PW?«is'*
^5' is,, an advaa^ge.|p,.it,,j^tjih^s^jf5nr.

'If attf- lieffons' reittatrt 'ft»d*i!^V^'ftfe«<^
What I havi faHf^M'Hmft bifg f&'Sif'iteidtf
to=^ fiirther ar^urteht." - • ;4'^"»q ""- ''• ' ••

(ere referred to, is the ijiQ^ wkh^that wbiqh^tbis So*"
Ciety has fincc fonowca;,an3 Tarn afraid t {Ball not be
^rb(Kt(rd, when I iky, thatf th^ trakuiatibxt (!b ^rove ha ca^
93^^ of fupporcing irtdt^ is foaaded eii d« ilp^^eion^
that a. hundred manied* opf n^ whofe^cMfHpa age ia 36^
will leave but <?«^ widow every year, tho* at the fame tioie
k is fuppofed that tWo of th^m wllrdii; cvefy ycarJ
\ Thiv miftake has made the whole calculation one half
wrong. — ^Nothing can be plainer than that, if the death
•of a married man d^ea not, leave a widow at the end of
^he year, the reafoh ihuii be^ that both hioiiCclf and hit
wife have happened tp die in the yean Bat it <is^aivray4
very improbable this iEould happen* , -,

(a) At "^pir'cent. the period of doubling money by
cQippound intcreft, is nearly 23 yeais. At 5 p€r cmt*,

It

and Laudable Societies^ 8cc. 7^

'It triuft be' retkofled opon that every other
member of the^ifooieties^ foppoAng th^m fo
con^ft of perfonv dl of the faUM og^s with
fheir wives, KvilMeave widows to whom, oiid
with another, (as already ibewn) atleaft'28/i
fer $nn. muft be Ulowed, :for a^ many yean
sis tber^ have beeA payments from«ach mem-*
ber. ' For every 10 guinear rben • rcecivcd
they muft fome tihie or ofher ficrbaftet ' pay
ft 8 L But let it %e well confidered what caa
enable then> to d» fhlfi, j Did mqneybcaf
ho intereft, for- aft y'gh^ettfhrtsnntow received,
they could not afbfd^at afiyUitqe horeaftef
to pay more thah^att '-^jri^/Aim. ; rTi^it iaj
(fitKreuhe durbikJ^ ^yiirtaHjaf^iji'iBnn the
pt^fehf cafe, b^<^iftffti II, tqiial4^ the>diJ4
rzthmdt marria^) the j^peri^bnfidemtida
for aAy given re^fcraonify anquity^^ to inf. al4
\bWtA to all thcf^>viv^$ of'a &t^ nvakiiagesj
woiiTd tie, an e^i^al'-a^Miity pa^bfe by each
marriage during xt^ exifteifcb/^ aiid juA half
^hd reverfiohiiry bniittNy, if'itto^loifattQdlaWed
ohly 'tb half the fbiVivbro, ocr-tw widows ex*^
i^l^^uveof Widb^Ml' *^lU-a»mifa]r!:p&ymoirt
tl¥enp!f^'z;^^uin*Mvduringi|i^ <;itfieo'^
tltle^ Wido\Vd:to'Uo ftM^ thtti^o ^naoi^r ct
r<^ 'guineas, fu]^0fiHglli6fieyiiC0r^caii«fro in^
oifilt, Bui if ttioney does bi^ imeoBll, tho
kkrkk payment wili-esititlt thein^to l]Qbre, io
proportion to the degree in which it is capa-
ble of being improved, durihg the tiAie be-
tween that in whicK the* annual payments be-

. gin.

76 cy the Londtfn Annuity

sin^ and the comnoencement of widowhood*
Now^ it is eafy to fee, that onle& money bearg
very hi^b sntereft; this improvement cannot
be likely in any circumftances to produce z
tapita]^ the intereft of which (hall be equal
to the annual. payment itfelf Any giyeq an^
nual payment perfectly improved at 4 per
cent, compound intereft, requires 1 7 years to
double itfelft fuppofing the firft payment
made ihimediately 5 or^ near 1 8 years {d)^ if
the firil: payment is not made 'till the end of
a year. But no marriages are Ukely to lad (b
]ong» except tho£b among perfons' who aro
very young. A marriage between two per^
fons, both 40^ will n^ frak^bly la^ Ipiigef
than 13 yeurs, tcpordin£t» the pro^ai^litie^
of life in YXu. Halky'^. Table. A marrij^c
between, two perfons^ botli .50^ will no|
probably,. by the fame Tabje, lafl longer
than eleven :jt!^%^\ noc.a marriage between
two perfohr^: both 30, longer than 16 years.
Such marriages, it is true^ m^^y poflibly \^^
30 or 40 yearSr ^pt thifi circumftaqce is
more than balaoced* by the fa^ that qo kis
pofiibly they majK not laft i^^< year. T^e a^-«
aual payments,. then> being incap^le of iuch
an improveuMnt as diall produce ao additi**
onal income equal to themfelves ^ it is qbvi^
0US4 that AOr^iety ought, to go fo far as.tq

#■«■•»

(tf) At 3 ^ uiu,\ the period of doubling mone^ bf
compound imercft^is nearly 23 years. At ^per am.
14 years. * • * * '* . ' . .

I allow

and LBJoABhLe Sockties, (cc yy

allov^ to widows annuities twice as great as
thofe which might be allowed^ fuppofing no
intereft of money {a) ; fo far, for inflance«
as to allow, inilead of lo guineas, 20 gui-^
aeas for an annual payment of five guineas*
In the circumftances of moil of thefe focie«
Ues three-fifths addition may be the full al-
lowance. That is; fuppofing the annual
payment of each member to be five guineas,
time may be expedted for gaining from hence
a capital of y^ guineas, or that mall produce
three guineas per annum intereft; and the
proper re verfiqnary annuity will be 1 6 gui-
neas I or fix guineas more than the proper
itverfionary annuity, did money admit of no
improvement*

The precedingN obfervations have gone on
die fuppofition, that the reverfionary annui**
ties s^re to be for life. What difference in
favour of thefe focieties arifes from the cir-
cumftance, that die annuities are to be paid
only^r widoivbood, cannot be exadUy deter-
mined. Some judgment, however, maybe

{g) Tht money accumulated will not be exa£Uy the
fame with that to which the annual pavmem wouM in«
ereafe, if improved at compound intereft for a namber of
years, equal to that which the «joint lirea bare an efiml
Atmce of exifting. Much lefs Vill the increaft be the
ikme with that which would arife from the annual pay-
ment, forborn, and improved , for a number of years cflua!
to the ixfi^fatkns of the joint lives. It mil be lefs tna^
dther of thefe, forareaion espkikied in AOte(L)Ap-

formed

y9 ^ Of the h^vAox^ Jixami^ *

formed c^it fi^n what latas jbecn £ud at t&dt
concluiion of Qgoft. IL Were even one hal£
pf the widows, to. marr^r, ftUl the firhemes: I
have beeiilf CQA&deting would prohablj beiii«*
fttfficient. . But^ in tli» circumflaoces of thdc
ibcietiesy it cannot be cxpeded, diat above
OQC in 1 o» or perhaps one in ao, will. tQSkvtjm
The per£bns moft likely- to enter into thcmj
are fuch as^Jiave not the piofpedt or 2hiiktyt
of making competent provifiona for their sur^
dows in ochec ways. The widows left^ thpre^
fore, will.in.gener^ be on provided for> tod^*
being alfi> tdft wiidi fiuniiies ofchildrent i6
is quite anreafoeabio to exped^ thati angp
confiderable proportion ihoold marry* This
is true of fuch as may happen to be left
young ; but when a fociety has fubfifted fome
time, the grektir piart wlU not be youxf g wlitn
leftt aod dude, at the fame tuae fAoit no adtf
vantegecatahe-expedied from their manyiog^
will be in general the bigbefi, annuitants^ and^
therefore^ the heanjitfi Sttra/ess. -^MortowsUpi
the prqfped^ of the lofs of their annuities!
will have a particul^ tendency to check mair^.
riagc anfong them. — For dl thefe reafons it
feems to me likely, that the benefit, wKidh
thefe focifetie's will derive from marriages*
among th^^r annuitants, will not be Yery^cp^i^
fiderable|i cr at leaft not^^ confiderable as to^
be equal ' to the advantages I have allowed^
them> by c^(;ulatlng on the fuppofitions/that
the money they rece^ will be ahtxys imfmv^
t^ ferfiSlly^ without lofs or delay ^ at the ratr

rf 4 par cent, compound tnUrefii vthat tho
pRikibilitiw of Mfe amoAg males and femaled
arethe falM^ timihall hB(bands likewifc of the
fiune ages with th«irwiv6s» iind diat confe-
qtmntly the ^AriwHttifoi widows on fuch'ib^
cietiefr can amoiHiftb no mdra than hidf the
aumber of marfiageb jf ii).~«Wkh reipedt ta
die tail- df thtfe fu^potti iotis^ it dcfervesr to foo
particiitarly obfervedl^ that from accouniia
taken annually with gfeat care in Scetland, it
apficars^ that the widows bf the mmifltrs and
frrfijirs there {b)^ notwitfaftafiding the di-
minotion -occafioned by their marry ing» do
exoeed coniidcrably the number of marriages^

- (m) <:ard'flaittld to tadoen in dMfe focicties, not t*
^gf f9( t^ yroporti^ V vidowf that will man'y* frppn
the prppoztion thut maj hippen to marry during their
£rft y^rt. for moft of die widows that will be left at
ft* Wdll M j^suag I V whetifat *tbc greater p«rt wiir riot M

laWfEf Wl^t tlt^r ^wioMncf widpwbm^ ffter » (ippqMjr
Kas (ubfifted 30 or 40 years \ and, therefore, thoueh ppQ
in three or four fhould marry at firft, it will not be rea-
Ibnabl^ lofxpedp that half .fo man^ fbould many after
the afifire oT ihe ^iety become Ibtionary.

X^) ThfL aiiii^bar of flMirood.mMifters.and piofcfibrt*
for 17 vears, from 1750 to 1766, was at a medium 667.
And) tjpm 1740 to 177 14. the leportf have givea abpuc
3^0 ak the number or widows all living at one time de-
/ived from this whole body. The medium of widow^
left annually has, for the }aft 27 years, been 19^; and,
f5r 10 years,' ending, tn (he ^ear 1767, but nine of thefe
k^d married.-^Of the annuitants lil(ewi(e (about 160 ii<
Aumber) oa the fund eftabliihed among the'Diflenters .ii|
LinJon^ for lelif ving the widows ^ indigent minifters. \i
k found that few ever marryJ See Chap,'^- Se£t. '2. See.
likewife die I^ttttr epd afthf vK^I? ^ayj. aid not^j(*i^J ill

theApj^9«a^. .;;: , , ;., .^ ^^; ..\^ ' . ,;.,..,..

^0 Of the tondot AoaUity .

And certainly it w6ul4 be uorctCoiMi^lo ini
thefe foQcties not to reckon that the ikmo
will happen among th$n[i<-t*Io4t^ it kaoA
certain^ that notwitl((kndihg the hamrda
that attend child- bearings the probability^
that the woman (hall fprvive igi n^arriage^
and not the man» is much gredfet (4) thaa
is' commonly imagined. It will be flicvm inr
the lad EiTay, that it is not leis than the odda
of 3 to 2 1 and had I calculated ^eeably to
this {z&, the values of annuities for widows,,
would have been given near a quarter greater
than they have been eiv^n on the fuppofition^
that the chance oi* (ur^ivorAup is equal h^
tween men and their wives.-<--It muit be ad-
ded» that I have made no account of any djc*
pences attending the execution and manage-
ment of the fchemes of thefe focieties. Some
inch expences there muil be» and fiime «1-
vantages fhould be always provided in order
to compenfate thespi.

There are in this kingdom icveral inditU'^
tiohs for the benefit of widows, befides the

(tf) Partly, as ot)rcrved in |Mt2e $, o^ account of tbcf
greater morutity of males, but diefly on account of the
cxcefs of age on the man's (idc.-— According to the ptin^
ed articles of agreemcitt, the Laudabk Sodttj pays no re*
gard to this excefs of age; and the allowance reduirej
On this account by the Londm Jbamilj Society is (0 tri*
fling that it deferves no notice.

In March 1770, thirty- two huftands had died in the
tofidabli Sodsffj and 27 wive^. They feem, therefore,
to be already beginning to experience, that' the chances
of fHTviforlhtp in marnage are in faroor of the wife.

tWQ

tfb'M-WHifeh' T Invfe Wfew rtbarkWj at?d iri^ .
gt«feraf, «U far i»l /jaVe hdd any''in/orrHattidfr-
c<«ftfehi?ft^fljete; mtf are'foUiided on plahi
eQttAlly ihide^iwttf; ■ Thef mdtbcsVTiitn fn-»
ffiferrcr ifie cbntrlVA-i .6f f hcfe jnfKtfaHdris-arti' •

thiift/ to have ^rtfertfied- • fil'emftffvfes Bettelr /'
im TOeaft^fffekftly-froftf v^hatlias'Bceh'*
fa!^{"Bilt' r'win ';uffl[< bifention d/fe 'furffier
p^ft#6Pit.'"' '■ =• ' • '• "■■"■'■ • ' ■•■ -• ■• ^•' .*

if Sff^;^^^ 5tears,' a-mil SpHeaf Ihjf thfere has' ^
bttri"illf ildri^ afr khnd*nii'f/!6s Iti 'favBfaror

rJfffinglKif i7»*tf//iWV 6t ifi trnkih^Htiti'dhhuat
f^mlW ''Ndw, ihey rtiay tie! affurtJd;' tHati^
ifit ^Jfeerid «f rtieff periods^ they (hoald not; •
bi?*B6RS!^d of a. coiifidcf aBle fui'pltfs, the truci

H'wSi'hty their hating granted much',
iri^hef ^^Irtiifrtici thart the annual ebrttribu^!
^^ft' dBle ftefniarifefitly to fupport": Poi'
irhas^befeh demonflrated, that the' nfUmber ; ;
bfanti^itants^and confequently the amount of'
fflB'ittlrfttSI dipericcs; wilt go ori Intireafirig fbi*
fPi^f/g' coiirfe of years beyond thcfe periods/
Ifte elftfit, ihcrcfbrt, of carrying into exe-'
cyitipft'ttis Tc^^uhtiori Will bey precipitating'

* "itfbSflkruptcy which would have eotnle too
W Kid *thcf e been no fadl reifulatiion. '

'^f has beeii feid in- defence! of thefe 9dd^^ •
tfl^s, thrat the deficiencies in their plaint ^tonot
^ of qnnch coni^quence, befaufe their tttks
r -• ■ . / G oblig*

Sfk Xif tbe LoihdQfiAniittfty .

obKge them ;to prpierv^ a. c{>if%;^: (|<|inlif)|*

bjstweeii th^jr iaconx an^ p^pepf e^ ^-li^-

<iMicing thesmpuittes «< tfaicije ^^bc Q?fi^$9(|.!

An4 K«rp.,hief»cc it i$ i»ferre(lr tJM^t tft^iCf^)

never l^c in any -danger of a t^|^pfiq]^«H^^

a^fPKer tp this, ift I)aa appeared, fl^t tl)f 4?fif9f/

when t|i(ty,;wiU begin to-fi^l d(^ptfni9ir8>.^t

d^ant, t|iat it v«{iU he t9o4«fe tp^««^ir ffft

<"■<>»% Y»WQ»^ finfe»Pg% ?nj|uUi« ^Jpu«iv:«
as to render them inconfiderable an4|tf;tfl|y9£».

AH .t^j|t sa jgiycjH ^op ,^ex^ to ^^/:ip-

n«»»<»ptt .^ 6> «»»cJ^ «i^R Vfm-. Iw yt^r^L

. . JWHfflh

wlio :caw after] th^,.; pe^^iient fi?h|^J^
thceefote,;.:^, att«)de4 fflfit^^ garti^^y flfl*/
juftic^; and! this inJA(yf?si;W^U he *&j(^^
*6 infte^ of //5dWi>^,t^e^wfpitie|5, ^a^^n\^
paympat? ihould bc,inci|e%i f fqr 4l,thf ,f%i

injwi^fe; to faU cqftfturi <'fW»^%'flr««» 4afef4i

of Jit fHTf.Ofl^Ufta^ttiS^ : ,

fittf W%, req^rc§; 190^, ;tp h»

Vcif, t^j;,; a!ft^r,ejtl^e?..the^iy»«i^s.%0.
heen. for fome time in a^ iksm Qf j^^ifi^i^f^
or the contributions in a.ftate ofimc^ff;^ i^,
will b^' fei^ tW thefe Societies h«^,,]
upon wrong planf, 9fidf therefore, x^'^j[
he delcrted and avc^ded ; the coafeqi^^iicf )(
which^wiU prove ftiU gi^ter deficients ^i%

theix

« • < « «

* •

ftrti#d anddeqliAer'tiy « total difiloliitioti
And bihkroptey fldM^plMeM^^^Oli^ he ttid
imth ^ AHoft 4»r^« fiiiifeik ^iiftiea^ fbt> j»r6^
irking for wii|pMi,'lt UMf ^ntiaue to be eti^
to«Ma|«di^ Mld^la Metf Jfoefl ^r Ihtvt^ j^tiis I
And at that period the number of MfMM^##
will be greater than everi whofe anouitie^^
having no othil fuj^port lh<h the poor re^
maina of « ftook always infijiAcieiiCy will l)«
foon left, wlttkout ;th« poffijbjlity of relief^ to
kmeAt that ignorance and . credulity which
^ave rife to th'eie ibcieties> * and which liad
f&J^ngrfuppprted them. '. ^ .

In the London Annuity Socipi^i there is aft
encouragemcQt to Batdilors: abd laidrwirs xa
join* them, arifing froin the aaditiooal an^
nuittes to which they wilt ^ mmiM^iftl^
entitled^ when they marry# lO coofe^ucncel
of having made their J)ay adepts a greater^
Dumber of years \ and it is imaginedt ^a^
particular advahtagits will be defived from,
fiich" membersi But even . thefe will in ge«
neral pay much lefs than. the. value of their
«BptAAtiona»f^A per&m . who . begiM^ m1 im«!
MMd oontritwitioD of fit* ^fineits af the z^
pf 24» willj ihould he livd 1 1 yeairs^ and marV
ry a^ womaA %;i tlie iame age at the ead ^
^bftt ttme^ mutk her imiMdisEtel/ to t^k
feraufu daririg furvivfltihip, and to ^iLpif
Mftum Aioylcl he live fouk* years afier ma)rr)F^'

$4 . Qf/J^ 4BkMeh»^4apng,

i^g, ■(int9rc(( t^if)gf»t4/<r\^<«l->' («). lo this
p,^ticv>jlar c^ ^therefore; :».ip«|-/bo.>.wiU:}M^
s^e^rly tl|4,tn^:vaUie.e^,I)rt .«](p<^»tion. Bat

who ir>»; in ^«rftCifn6,^»ii,«j/^«r»;after.4d-v

^ * '

. • • •

• 4

• . 14

Of tbk Ayoctation among />5^*tbridfcn^,C^^
^. 4/?^ /i6^ MintHers tn Scothna. for 'provi^s
, Anniattesjor tbetr ns^idows. ■

• • -

IN. April, 1765, the dlergy3yiaiiii the pflls
of mortat^ty ; and the qo(i At j^; of My^/Q/^x,^
at i general meeting in S{on'^Cmege^ agreed to
form themfcl^es into a fociety f6r *thd fub--
port of their widows and orphans. Many in
ftisTrfpei(ftibl8|b&dy may be capable of do-
ing, in'a fccttefnianiUr^ what 1 have attempt-
ed in this Treatifcj; arid 'tHey are, perhaps,"
^f cady fenfiblc pf the deficiencies in the plan;

' . ' r ♦ • ^t^m liTi^ ■?

(a) The value of five guintas pet dfinum (iiVft pxfhtni
nade imowdiacelv) for ii fears; flifa^tdfail^flkv^Fd^
^ life now 94 fJM* t ?l»d» a6er I i;ycai^|, fcjRjUnejpiQC Vm^k

p^dent value of 35 A /«r

pdrfpn myrr 14, fi^uld he Itve^iliyellQi^imd QUtfry a lm^

0490 of ttie fariserage with himfelf at.tbe.^d of that time^
and ajib of 6/. more, or 41 /. pa* annum ^A .aI^« ihould ne *
Iht'at^ermamage four, years ; is, by the Table otLanStf
Q^cvationt, l.b^.'3ll>.^hfDTkJHalUf% Table, /. 76.03.

which

'Xi^

the London Clergy^ &c. 85

'which they have cftabliihed- I fliall not>
ho^^c^ct*, '1 hopt, do wrong, in taking the
Kbcrty to recite briefly this plan, in order to
ifetroduce a few obfervations upon it.

According to the printed articles, every

clergyman poffeflcd of any benefice, Icfture-

-ihij),' or licehfed curacy, within the bills of

Wdrtality; and the county of Middle/ex, who

'^fwbfcribes /annually one guinea, or two gui-r

il8fs,*"0r rntK-e, ' fli&Hcn title his widow to an

*4nhuity j or, if he leaves no widow, he fliall

eiitkle any fuch children as he fhall leave, to

the-<sltrie' aortuity for feven years as his wi-

^OW wduld hive had. . And, in cafe a widow

}pGfkikA of ah annuity,, fhouU"'^ither die or

riw^^/^K bifore the laple of io years, from the

<fomiiSencemehl of herannuitjr, fuch children

t>f'h«f former* hiifban a, as {harl.be then alive^

are to* be entitled to as many of the ten years

•paytnentsf of tfit annuities as flie ihall not

liave received .-'^-The ahnliity is 'fixed to no

particular fum, but inftead of this, it is.or-

•dcnEid, ' that a fourth part of the annual fub-

xfc^iptions aiid intereil /hall be divided the

-firft- three yeara after Ac eftabliihment of the

fociety ; half only the next four vears ; and

•;j-4thtf the ttext'frve years 5 provided^ however,

rthlt'in no one of thefe 12 years the dividend

^iMHi exce'ed 26/. to the widows and orphans

«0f die elf rgy fublcribing two guineas brnrvore;

-^ndW^J. to thb widows and orphans of the

fubfcribers of one gtlinea.^ Attd, aftie^ the ex-

rtl G 3 piration

8^ Of tb^ 4fi<^tm jfU9S

piratk)n ofi z y^^rs, th? who]e aq;KHinVc/ (lie
filbfcriptioa$^ and of the interdft of lii9 «tpir
tal fkoplc, is to be divided prQport|QQablf »fi)f
f ver-— If is further provided^ U)tt every ol^arr
gymaa/ who fhaU be married^ or l^ay^^ilr
dren> at the time of his fubfcription, ihall p^
a fine of two gqifteas ^ward^ a papitai i^c^
if ^ fi^bfcriher of two guineas or mc^re, md ^,
years of age or upwards. If 50 years, of a^
Or up wards, he uaU pay a fine ^ rhrt is gi^i^
lieas 1 if 60 or upwards^ 6yp guineas. P!M« if
not married at ^e tinaeof lii$ fubfqribifig^ m^
ihall afterwards mvry^ hp pf^l pay s^ ^e ac^
fording tp thje age hfi ihall be of 4? the fiaio
of hi^ ' iQarrying. Thp obligation lai4 |ipon
alU whether ci^^ried of unmarf ied^ t$> b^oplf
lubfcribers^ is^ ap iAcapacjty of btii^g ad^r
|ed members j^ithout thp co^f^Bt q£ a gjmer
ral frourt, unjef^ within tv^tq y^afs aftef ber
froxnin^ poileilai o^ any eccleiuifticai employ-
inent,.lliey iubicribe^ ^ . . -^

• ■ 1 « • • I • ,

jrafioos la t^us a|i4 t^ prec^dJR^ ^l^tPlor*

muft'lcnow vfhat iu^e^K. I^.iqrift W ^f^

tct w fiipppfc. .tha* #. the cUjcfjr- liP Zi«»-

;^j» ai)d[ Mj4Mefe:f 09x0^ x^yoi ^ti» AShHinKi^

thcyAafie Ailjibrihf<rfr of :tW^^#f|«flfc^^^^
, and th^f there af(s %q(i9^.th«i9 M dnRgr itti»r>
qiarricd peifqj^s fs iaMr>«^ - '. - . 'ip"-: i-

*•"¥<! *lJrt« iaft,;it ftiiay be learnt from .Ctu<5ft.
jClJf, that tl^e ifthriuity to wj^tch widows
Ihcrn^ be entitled^ (fuppofing no allowance
to the childrdii bi^. any that die) ought not to
hki^t6A Ijo or 1 1- guineas af moft. and that,
Dt;&les.the annual fubftriptions^ there ought -

. to iAyk been a fine paid at the commencement
'ofniK icfaeiile» by every married pcrfbn, of fiaf
gofnea^ at lea/l^ Or^ by the whol^ number of
iu}>f<brjibers» thi'ee guineas. If the number of
tuairi^^d meilnbers is double the unmarried,
tiie jiithuity ought noi to exceed eight gui-^
ibeas;. and the fine from every member
flioUld be iiboi^ foiir guineas, — ^The order,
rhdt'bhly a fourth pa<^t of the ar^hual fub-
foiplr^ons ahd int^reit (haf) be divided the
fim three years, half .&e iiexf four years,
amf thfcfe' qditrfeVf thi iiext five, is with-
out ' f^eafon i beicaiiie the number of p)ai«
mdrfts, fd^ the hv& i i years of the fchenie,
MVht (6 feiiK^'thaf it win not be poffiHe,

^lirtiig thai fiiiiei that there flibuld Dc occ?-
fion wr (ftiriUing any propoo-tions ip large oj^

. che ili/i<id (bbicriptions and intereft, imlefi
they are indeed beyond all bo^mdsiob little,.
— After 12 years, the number of annuitaots^
^jffi ]^o off incteafiilg ^r near 56 yean, a$
ftppe^» itiMi Qidte^ lH. The coa/eq&ence.

rflicrcfprfc, 6f:diVjdihg; after that tiihe, the

, vih(A&istko%m6i^e annual fubfcriptions and

' mfettn^ wilt be a conftant yearly diminution

lii'the (Ji^icieiidt f6r near 50 years ; ami mak-

> - G 4 in^

^ Of, tife Eft^i]^cp t7^»9i^jf

l9g 4^ payinpnts to thfi.4rft:cl9ima«ts.mycl»
tnprc cpnljdciable (han tl^c^* PMghf to Wi ♦ tt
the .expcnc9 of ajl fub/eqiieqt <jlajjpai>tSPT-'?qF
(Ijefe rp^ons j, it apftc^r?' to oici .o«t of, alj
dbubtj t|iat this (^^heipc is by pp piejins llkply

.. to aniwer the ^oo^ ends prop6fc4 by, it; aii4
that, therefore, it will be beft tp laylif afide^
At: the jinieit was f?ttle4 it was^ I find^,fiif^
ther ag^reedi that the annual fubfcr^jptiojii of
the/^/Zy, together with th? Jntprcft. oif their

. benefaftiens,' j^hlefs otherwise dir9^e4 by thq
d9n6r5yah4 thie annyaj fubibriptioos of fucli
pf the clergy as fljall fo/4lrc^i . flxali make a
cbaritapk fund to be ai^pUe^.tOithe -re)ief qI^
the diftreffcd wi^qws pr. cjjjldren ,ofr ^Lthi^
clergy within ',thp linuts I,'hay^9 mcntipnedj^
^vhether fiibfcribers 9r >pi^ * pjrQvidfd. iibat,in

• no one y;ear of the fjrtt Ivv^vt^to 29/,

be given out^f the fj|nd tp anvi one famiUj,—
This >s^ an expellent d^figQ 4 gnd if.^he ;no-
- ney aniipe jtrqra aUthe^upfcfjptiions 1$ tiirqwQ
, into thiji Cupd^ ; an, linporfent ih?ip.s qf nlifjir
P^ay. ??• BfPv^'^d, for fucli 6f.flie .uio^e.indin
fi^'IfT'tP^'V^^ famihqs {is Wijl j^c9<;gjt tBfi ..
heJp of charity. , ,. - ^ , i ,.

■

^^e k^4 (^) W th(» kingdom,- Iwvd toa -
^rnije^ ;<l$b. ^P ; ^j^^l' oC this : and tbe iiic-
f^{f\ With^w^hijch ib h^ |;>eein hlthctia atteBd«>
f4, i^roqe. of .;fh^principaj causes M» whicll

vtoffcr ^i^ipii^give foiae-acQoiiBOf it; (U)4 T; .' -
}t.Yfi\i, ^,4^fficicnt wl^h.this vi§w to vopn^ .
tip% 'Mhjit^fQK ^ afi^ual paymeqtt.wbkh- '

*'. J^fti;fc <:Qnfri|?*>tt?ra, 1^.7 pf whom are, mat- . 1 . '.
ff. rie4tperfofi8,,l)Qy^de# ,*. iajf -on. w«<Wii!g»t ," ,

f*.ey.erX'W^¥Jpwjqfr^ani?,«iiyf)f.^ A, during: . .

'f . VKJJdow^pal, ?w<i;aiip «M?ry^ laiuily' of «liil!' . .
'' dren that (hall be left by Cuch.lgacmbtit- ..

([«,.4sj4jp3^jt|^pM ;iwv«gj widow*;' tor'aoQ /."
T6is Jf l^foe fooii^in^ ^ yjiri^ty-^tfif her jiai*
ticifl^s f. bu( ihis; is . i^:i^bjl^i>c«}rTrI« coiair
fricr^Jd-'ipql^.the .2j<]» ofir^tfreti, sjif^i.mA
jfrpoji ,^&a$i j^iipe, tft. tjiaj^ict pejSfewteArt^
f77!9»o9''nin..a,6!Uea?f,,w4;.p^ih58 ln.<JlAb«»
lS^i,^(^^hi ap4j-i?r<?feffo4^ 4ifl<W i»d; ^ft

'4

.Society, tho* ^is. p|ai) is to^Uf di&renf , profj^e^-fa (or^i
jtfcif on the prthGipTcs of tne ^c j/^^ cftabfii^mentjj aii^ to
^priyc cflf ouragcnxe^it ft:om it, , ^

31 *■••..

mA the tntiMSi siA^i^kMhu to tliiiq^ ^ii^
' 0Mtekm htfsA ittzli SUbtnd Uiis fitiali
fMito ^4. jo/, thtt Wttlt tftnUitA ifacjdfat ; ati|^
^ f«l»dk>d<ry 6r 43 1 S /. per vHri. \fill b^
tbe Aiflidib^ |»rovifioti foir bearing thb «(;<■
Mte {rf^aU tfit aaivUltitoii poffiUe to bedli^

: *. f i«^ irim «67 liuinlag^: Such kA afthtial

. tfaytteiit, or 4«.27 each ^m 101 r cdritii-*-
;bofOffi,<i|| the UaaA VHfh 6.55 «ai:fi,. i)*6a&

< • - 4ftfJ o m r i ftflitors i itiid,. eonfisqiientiyv it iaj)^

. ^tm, ihat in thft tftabliAtteat a c4dtt!bu-

. l6mM received eii)iii<ra]eBC to an aMiuitt riay-

IDUtfrbdgiiMiiiig' iMidtikt^bly, 6f /; 6. 5^ liroitn

. WHOlf maiti^ .miMf, in order to ^nwM his
'i^^ti KA 4nniiiti^ of 20 /. daring hd' Wil

• Itf the S(»d«^t< fii«nti6fied in tlfe^fi^-
tifrfi, annniliei ultirtafiag froM iidX'ib 4t> ).
af«< pMmiied to-#iMws fbr an ahmid ^-
JWiM ^ 6nly 5 gc^Aeisiftf); Add, in' -aQ
&fi IbCffcdef for ft« knehfe of liiridofws ilirith
«»4ittiiil ifnf flcquaifitted, die^i^ an tq^ ck
H-gk-daMT di(^rop6rtio» bfctWeen the ^ontriba*
tidiis ri««iVe)df, iMd^^a^hmties pfdmifedf.-^
Willif^^hat' AriAg« Hdtiii^ liick ^ar th«
plan of this eftablifhment been popied ?
And how abfurdly'^aTe the ibcle^ W tiiis
jkingdom pkade4. itsia a precedent wiucih •tan
cocrtagea and i^vonra imaa?-plt '*frdaW b^
. »illj«g to % iSw^fit ofa tWs fulij^.

I » • I •

I ' > . •

(0) Seepge,67.

It

-r* It mt)rbfe^obfenMd diM (he tumral'MCOifeB
.:^r tl)iK fnpport of tbi$ eftad»Ufl)ai«nt#- fMfl^
jfQ^og a. to hnvo only |fa^ beiiQfii:i>f wt^iem
4a vif\Y> ^ogbc be1iL7^.l^ ,/k^ Mir. frocH
f?vi9r)r ' ni»riiagi^ aqaOfdkig to Q^oft^ XUL
Pk 44. 'itad /. 7^4 ^ MMi. ncoordidg to tl»
^lpitlati0n ia Note F» Ajppcndixi •

TbejfeicktofitintietQm exceed tbo incocne
^lolily provided « fitrt die «]Goe0b^ aro by
:^o m^an^coofideiable^nOugbr toafferd iny
jPfptaiR ireaiopf for conckiduo^» that cb4 fdM
pf 't)ii$ «j(l|ib4i(htneK ,wiU prove infuffitieal.
;! wwf,,' ^pwever^f QnCo M tQ dMuertain fone
4oiibt« if0 thii ^ii)^. And in Iribffi^ deiibtB
{ draili^t liiyfciyr qpn^rmei by obfefvm^
fha(, » the i«»)isit]a(iona: (^) fxidde;at .tfe
.poixH9en<«mefH <^ • the icheiQc^ thct mimber
33S ^^ i^M» as tke ^murimMfif of wuioWB
Jwng ! af 9ae tiQ)«, likely t^ come «fok)tl k^
:pr ^p ^ 4"?i?e4 from 20 (^) widows Mc
aiupta^^i ami alfo^ tb«< 4P yiesm iraaftated
^ .tfa(e*|i9aibcr oiF )^alt itecliifiary ite beiag: on
i^fMjf^i^^ ^erea»Jr:«r4alati(fied, that

J?

« P^mdy fiTr 4 frovifionfir At tviiswiand chiliren rf tSf

aii<l progrefi of m Fund.

nrjfe the note in p. 70. ':_ .; ^ : '

•.i . I -the

• • •

« .

92 * •'ty /i6^ fiflfabliflimcnr tfw^w^ /

the malcmum of widows* would nfot pibvo
•snuch Ms than 400 j nor the Aumb^r of
>jrcars neceiTary to bring it on» lefs than 60,^-^
In the former edijtk^n^ of this work, I gave

' ^^diftin6t account of this. But I have lately
fcceivefl ^fuch information {c) as has con*-
vinced me • that xpy doubts have been in a
^reat meafuTC groundlefs. I have learnt^ in
'particular, that tfiere faiayo been calcuUfions
fubfequent to thofe I had ieen^and thatthis
^eftabli^ment has enjoyed advantages and
•l^rovifiohs for its fuppoH which I -Was unac«
^quainted : with; > and^ which- -give fiJaibA ' i(k
expeding that it will indeed be 'able to bear
•the expencc of 400 'anniaitants, ^ould ^
xhnny* come up(Mi it; I (hould 6nly «f re«m<>ft
of myiwdcrs^ wcite"!' to eWter into an ac^
x:ouht'Of thefe advantages^ and provifibns^ ; It
iWill fae^ of miore importance to take this opi>
jyettenityito obferve^ that die probabilities of

* Sife Yram 'Whi{:h the - determinMidns i have
ane^tiofted sire derived^ though inuch -lower,
iriiflki 4he ptdbabilittea^^f lift among the mi^
niflers and their wives in Scotland (^Z), -
%rtyti' ful4i- as give the values of rcyerflons
'^^P^<^3ff^ ;on among: tlwp. ^99

(t)' I owe tf^snnfemiatiojrt to the UnJ and very oblige .
irt^ '^toidduf of tbiJ 'VcvAcfli and*ingeiuou& Dr. Web'^
STfiR, oi Edinburgh. : - •'' • ■ '"< '^ "-

-:; . Y^vMere: paftn^d W oocteei li#l hh\3A!titX tfiisVitif the -
conclufion of ihe laft Eflay. •'^: . •*' »*• «» • *« '•• >•

• « la

tkf'Moii^riii Scotland, kdi ^f^

*

vtil tirder to cmderftand this, k mvth he^
Gonfideredf that the diiFertnce bdtween the* *
^btUliites of li& in diiFerent fituations/ /
aketphtce chiefly in thc-fitft fttid thethiddld^
iU^ of< life; and thatm ^6lA dge^* they arcK
imriy.thtf fame Ih aR fitunibris. ^ This rnkf^
berdedoced'vrith abinuiant <ltidene)i f¥tnfh th^^
thwe^firft Tables ih ^ Supplement fcofittipar*-(
ccbcwith' the two ^; ^aM 'with the. T^Ie o^
dWcnrationg for'-Lo^D«^w/ The » cflfeft * 6ft
liiit m^ift be to. inic^eaft't}^ durttioii of /i^/xif^ .
/kjri, iisidiat:. the fafiieifitn
rti^thof^^Jidrvivor/hlf .Jli Uhofe fithiriqhi^
whidi aitermoil'fafvburaUe to hcklfh. -Or/ •
io' other Vords,: tx> Vender^ the duratiOri J^^T
mkrtitigtP in^fuch fitc|alk>h$^9*^ greater than'lt^
wotM'Otherwiiirbe jn (prc^rtion to the*du-^
ration of ividowhoodi and> confequcntiy, to^ ,
reducer thd pf efent vialoe'in annikal ^ayoifeots *
daring maAiage, of any givtfn annuity pay-^
able dtnTing* widowhood. For Infkance. wereF ,
the pnibabilities of ' life' among ' the tnihiiterd^
Mtt^lheir Wires iti ScoTtlA^D the fanle thati
^ley^re in' Mr. De M<ni>re's hypothefis, dr*-
i^grablw HI. IV. abd' V; in the Appendix,>^
th^^itaitibnr of matriages 'aiiiong them^ fa^^
kon iDtie'witii. andt^f^-coiitd not* be liiorr^
than 19 years. The duration of widow-
bMd wpuld be' 22^"^ years, and the 'i^axlmOnu^
of w^(Jo^*rs ' Uving at one Jtime derived Ci^onir
6i6^7. marti^gps caonftantly iiept up^: would bt^
coniiderably more than 400.— Were-thepro-^^ *
< ^ 3 babilitic»

liagis; jDiro^ ibi^^ftjUf/ffi, -mtl the (knttiinloBli
^46^^ grf4Ur» inil. tlwi ffloKMitapiviiffi

Bf^rJI^if^th^o 5oo».) ihtt.lht'.fii^.it.ytaati

- ^ rcVvwMoA ^ loamigff. AwArig: tbtm m aad

y£9^i^.9»/^ % half («) j. mM tliat.cif-:^idinrho«ii

ibpux 9aiy«^Sf,. , A<Mli:i( ' s^ppins «Ub|i iireite

. the .wlio^l^ bQ(^ of ffiiniiWs) «DA:iiMifeiliiMn»\
' U ^u^:$S9i Jt Al» tfatorsffirf^vXerioinf'tlMt!

f\|ipport of.thi^r^lv^fisifr'.lhan w6Qfai;bQ oisoeiki
fwy* wc^rdiiwt tp tJ^. pf^sbslitica of iafviiiti

PRRTP t^rp^rwAnowt, IjotuidttiAJni-of: thtLiitfiftfr
afi^e tQ dire «M4^0«>'(U}4;^/i^/9d-iRrii(cktt'lnrf?

r r

I I

« *

]^y&yi6t4hy tht'trdMitt left'iianurilytol' »9.z) gWar

iMpit WW/i^ i»f.,.i Tljcj^ar^ «fmn<»^ »Ur.
^. 4^. Mve l^ftlf fpflnd.vf apy «»%»»rtoW

' 1

I . . . . , .

•' •> t A * III C "t »..11JI

' I • ^

• r r '•.►^« ■ t . * • iw • » ,\ ' * • f*' 1' • ' » I . ' ' ♦.' I •

f *l ' f ' •

•'j'J' ' ii'- < .I'l \-J^\19ifiSPtf*i''- \ •■•;.:i!i!i • -
.\n.j\ *.u ,■■ '.! •.■•nO '. )- ••:,:.(.•/ ••• »

, inti^ifS: w^u^. ?ritly>i||, 40u%|«, :^ eg^

«RfiM)yi i9j«$fi9l^ a^fii^ jfiich b« qf qtriirfd w

and ituouragmg' The natures of thi^g^.^A

syi^ imgg ii w rt i - ThfHi)Miiti9Q{baD4 rnltKi

4fyia«mi«MS My ^R.jMQr0>«9t« ^^ 4«r^

jb particular^ it nuy be ia^rfi(ilh«i'(MI)lNQ#

V

V

I

]2fe ^ in Mry^^-JIfvf^/irli^iHdM Ma|ll#

for ih -^niidF j>a^ri!itlhl^B«gtrihin|firt{tftd9ia

atclf^ybtir "gd{n«i8"dttfr^'iftamtig«-'i «i^

1^ foil « = gcri Aci ' AiM IjaW liHi^/^ IHM

'<Sranl tif feach year^Wilhe^le/of.lil^^li***

lied i!httir,^n^i< '40^ fiilght-%e> e^i«Ki %9Vtl^

., aennaity- foi'-iiis' widoWJ dHHii^ ^/^H"^^!f^'i<^

. Be lives a' yeai*^ 1 d /. if 1ife'1»*e»'/i^<§'ytedMS?

' and 29 /. if he Uvesy?!)^ fiifkJ Mok^>i^

fcarcely now in this kingdom be improved

at fo high a ratd as 4.p/r centi Btftj perhaps^

It might be rea(d)iabiy es^^^i that an ad>

▼antage, fufficient to compenfate this difad<*

yaRtage^^\^uW M dtHny^;']f|.^.^4hjA|iA^

the annuities I havenHieMidilJIed into annuities

during widowhood. One may^ at lea^

renttSM'-'td'^ori^ttfli^^'filit'i'^Gmj^)^^

Woffe''^ouM"befaU a-^ifiibic^tMt'itrcMiQi.
i^is jpliihVlhafl ^tbe-'fik^fli^of idi»i& «xmW
olhei<'edditig'iialfi|i |iiik<ritf Xi^4ttft^ld2ij^

IhentS*'-'' ' :'J!.'a tiil'. .'j«isV.-\AO'*kVi i>oc

A^l hB^^'«6 0«nli#tftfl'A)eiiit»iHl'iRt lk^
t!fk iv^i^^^l bb «ni^M<V«SKll^r^^i««
ilUities/iik^tiiHea^, id^idrta)^'«ft!<t)«6biljh«^
payments -0.% adflhifliptl/ 'i«to\iltf t»^ i«l!d»fWI
^ayinen«fbf «n am>«tty(«f<«5iC «ntf tii<^a^
nea's for ah • Annuity ' ^ • 30 /.• ^if t'-ihiim^
AouW liv«'»^ y<5ar»«i ^ ^ V*« •- »--'-vbwq at
'. • ' . .All

providing Annuities for Widowsi 97

All batchelors and widowers might be cn-
bouraged to join fiich i focietyi by admitting
them on the following terms. — Four guineas
to be paid on admi^^oh, and three guineas
every year afterwards, during celibacy ; ahd^
^on marriagci the fame payments with thofe
made by perfons admitted after niarridge;
in confideratiori of whichj 1 /; per annum^ for
every fingle payment before marriage^ might
be added to the annuities, to which fuch
members would have been otherwife en-^
titled;

For eiamplc. If they have been members
four years^ or made five payments before
marriage^ inftead of being entitled to life^^an'*
nuities for their widows of only 5 /. i o A
20 /. 25/; and 30/; on the conditions I have
fpecifiedi they rhight be entitled to annuities
of roll 15 /; 25 /• 30 /; and 35 A Or, if they
have been members nine years^ and made 10
payments^ they might, inftead of the fame
annuities^ be entitled to annuities of 15 A
£o A 30 A 35 A and 40A— *ln this cafe, the
contributions of fuch members as fhould hap«*
pen to deferti or die in celibacy^ would be fo
much profit to the fociety, tending to give it
more ftrength and fecurity^

This is one of the beft fchemes that I am
able to think of, or would chufe to recom*-
mead 4 There are, however, others no lefs
iafe and encouraging which fome may pre*

H fcr.

^t Of the heft Schemes fit

ftr, and which therefore, I will juft jpro*
pofe.

Let the probabilities of life be the fame
with thofe in the Tables juft mentioned^
Let money be fuppefed to be improved at no
higher intercft than 3 per cent. Let the re-
verfionary annuities promiied to widows b«
10/* for lifej if a member lives five years
after admiffion> and 1 5 /. more> or 25 /. in all,
if he lives 'i 1 years« The proper payments
for fuch an expedation, from a married rnaa
not exceeding 50 years of age, wilt, in the
nearefl and mod convenient round fums^ be
four guineas in anntuil payments beginning
immediately, and two guineas in hand for
every year that his age exceeds his wife^Si not
admitting any greater excefs than 1 5 years :
Or, if the whple value is given in one pr^ent
payment^ 40 /• added to a guinea, for every year
thikt his age falls Oiort of 50^ belides the pay-^
meat juft mentioned on account of difpariiy
of age. — -For example^ Four guineas in ao**
Rual payments, betides 10 or 20 guineas in
hand^ according as the age of the hufl)Md
exceeds the wife's 5 or 1 o years. Or^ if tlw
whole ualue of the expectation is given in o««
payment, 10 guineas added to 40/. (that is
50/. 10 ^.) from a man wbofe age is 40; and^
in like inanner^ 20 guineas added to 40 L
(that is 61 /.) from a man whoie age is 50. >

befidct

providing Annuities Jhr U^idows. ^^

t)efidcs the payment juft mentioned oA ic-*
Count of difparity of age.

If money is improved at 4 pef tent, of ^ oft
Account of any advantages attending a fcheme^
may be juftly confidered as fo improved, (he
full payments for the expectation I have
mentioned will be about one eighth (or kal^
ti guinea) lefs in the annual payments during
ftlarriage; and a quarter lefs in all the oth'df
payments* That is i A married man> at of
under 50^ would, bcfides three guineas and!
half in annual payments during marrlagei b€
botifid to add a guinea and half for every
year he is older than his wufe : Ofj if hd
chafes fo give the value of his exped'ation iit
6rte payment) befides the common contrib'u-'
tion of 36/. and a guinea and half for ever/
year his age exceeds his wife's ; hd would bb
bound to pay three (Juarters of a guinea, for
^very year he is lefs than 50 years of age ;
(hat is, 53/. i2Ji bd. in all, fuppofing hini
40 years of age, and 16 years older than his
wife."^*-All fhefe payments doubled would
entitle to double annuities.

There is one particular' advantage? whicit
fociefies formed on a plan of this kfnd would
enjoy [a]. — PdffonS v^ho kno<v thenfifelvea
fubjed to diforderS, which ar6 likdy to ren-
der fhem (liort- lived, wHlha^e fto great terfip-
t^tions to endeavour to gain admidlon info

(tf) Sec anolhi^r advintage mentioAed under Queft.*
Vlu, p. 28.

H z fiicb

^

loo Of the beji Schemes for

•

fuch focieties ; and, if admitted, the danger
from them will be lefs than on any other
plan. Were it^ not for this danger, one
might recommend the following plan, as
one of the moil inviting.

In the plans hitherto mentioned it is im-
plied, that, if either a member or his wife
dies within any of the periods fpecified, the
additional annuities, that would otherwife
have become due, will be loft. But it would
be much more agreeable to a purcliafer, that
they ihould be made certain to his wife, pro^
vided fhe lives to the end of thefe periods,
though in the mean time his own life fhould
fail. The value of fuch annuities may be
computed by the rule in Queft. IX.

Suppofe, for enftance, the Jcheme to be
** that a wife fliall be intitled certainly to a
" life-annuity of 20/. £he firft payment of
" which (hall be made at the end of 1 2 years,
" provided (he (hould be then alive, and her
** hu(band dead; or at the end of any year
*' beyond this term in which flie may hap-
*^ pen to be left a widow." Suppofe it alfo
ftipulated, ** that (lie (hall be entitled to
^* 10/. more, or 30/. in all, on the fame
** terms, provided fhe (hould live 16 years."
—The value of fuch an expectation (intereft
being at 3 per cent, and the probabilities of
fife as in Mr. De Moivre\ hypothefis) will
be, in the moft convenient round fums, fup-
poUog none admitted above 50 years of age,

feven

providing Annuities for Widows. i o i

feven guineas in annual payments to be con-
tinued during marriage, and to begin imme-
diately ; befides four guineas in prefent mo*
hey for every year, as far as 1 5 years, that
the hulband's age exceeds the wife's, if he is
between 40 and 50, and three guineas on the
lame account if he is under 40: or, if the
whole value of the expectation is given in
one prefent payment, 70/. added to a guinea
and half, for every year that the hufband's
'age falls (hort of 50, befides the payment juft
mentioned on account of difparity of age.

If the annuities are made to be annuities
during widowhood^ and not during life^ and
the advantage arifing from hence, is fuppof-
cd equivalent to thje difference between the
improvement of money at 4 per cent, and its
real improvement ; the value of the expefta-
tion jufl mentioned, (that is, its value at
4 per cent.) will be fix guineas in annual pay-
ments ; befides three guineas in prefent mo«
ney, for every year that the hufband's age
exceeds the wife's, if he is between 40 and
50; and 2 guineas, if he i$ under 40: or, if
the whole value of the expectation is given
in one prefent payment, 56/. added tp i/. 5/.
for every, year that his age falls (hort of 50,
befides the payment laft mentioned pi) ap<v
count of inequality of age ia)^

He

{a) Suppofing 16 years the only term, the aonuitv
2t)/. and intereft at i^pgr am, the proper payments will
be nearly, in the cafe of equal ages and Jingu payments^

H3 ^6/,

109 Of ththeji Scbfws fgr

He tb»t will give himfelf the trouble to
palcuUte, agreeably to the dire&ions in the
Qixcftions to which J have referred^ ^Vill fin4
thxt, taking ^11, particular cafes together, the
fules now given- ^oine as near the truth a$
ihere is r^aTon ta deiire in an affair of thif
Dfuturc, the defe5ls in fbroe cafes be^ng nearly
poqappnfated by the excejfes in others.

I liaye calculated here^ as well as in mo{(
other places, from Mr. Pe Mofvre*s hypo^r
|hefiS| becaufe its conformity to the. three
Tables which I h^yp (o often mentioned|
poqvinpes me, that it gives a proper medium
t)etwce!i the different values of (own an4
fflf/c^rj lives, In the country the probabiliT
lies PI life are muph higher ; but in J^on4o^^
^nd probably in all ghat to>vns and fooie
fmtUl^r ones, they are much lower.

4^l'r^4oi: — 29/* 9s the age of the man is 3O9 4P1 or 5Q.
Dr, in ^HTffW payments, /.s.^o.-Tr-/.3.66.— /.3.13— Syp-
pofing ik9 woipaa^^ agfe 10 years ie6 than the man's, t4e
bmc yalf^cfs wiU (>e, in^Ji^/f pnyf»enrs, /.58.92.-r?/.5^,56»
r-"AS3;^-;-Io ^^^^ payments /.4.63;-?r-/.s '^*5.4K—
It appears, therefore, that «i Tociety, fuppofipg monejr
imprciyeiJ ar the rate of jj^pereent. might emitleali mar?
Fi94 fi;\t% indtf^miMUly^ who are under 50 years of agc^
tp fueh ap ^i^pcifl^tion as this for tl^ir wives^ for either
f>ol. \n one payment, or five guineas in annval payments*
fc^Buteqiiity require, that different paymejiu ifiould be
made, ocGotdi0g 10 the diflTerent comparative agesof mea
and their wives ; arK] T^ibles ipjght bf form^d^i^P (hew^
^M| at one view, what thefe ditTerent payments ought
1o%e in all cafes. If fuch Tables are wanting, recourfe
ir.uft be had to fpme fuch eafy rules 4s thofe I have ftated

providing Annuities for Widows. 103

h is proper to add, that, according to the
values of lives, and furvivor^ips deduced botlv
from the London and Dr. Halley'^ Table, and
taking intereil as low as 3 per cent* all wo-
iqen whofe husbands are under 50 years of
age^ might be in titled to an annuity of 24/.
during ^^ (the f^rft payment to be made at
the end of the year in which they ihali be
left widows) for the fiim of xooL fuppofing
3 A additional given on account of every year
that they are younger than their hufbands.—
At ^per cent, an annuity of 30/. might be
granted on the fame terms*

. In the year 1690, the company cX Mercers,
in London t adopted fuch a icheme as that
laft mentioned* For jco/. in one prejent pay^
mpnt^ they entitled every fublcriber to a l^e^
annuity for his widow of 30/. ; and this> at
thkt time, (when money bore 8 per cent, in-
tereft) was coniiderably lefs than the value
of the money advanc^^ fuppoiing men and
their wives of equal ages. As the interefl
of money funk, they funk alfo the annuity^
firft to 25/. and then to 20/. and 15/. But at
laft, after carrying on the fcheme for above
50 years, finding the bu^rden of the annui-
tants too heavy, and likely to go on increaf*
ing, they were obliged to drop the fcheme
and to flop payment. In a little time, how-
ever, by a parliamentary aid of 3000/. per
ann. which they are now enjoying, they
were rellored to a capacity of making good

H 4 all

Ib4

Of the heji Schemes for

all their engagements, and of paying thein
arrears. — Their failure, is, indeed, much to
be lamented ; for, in confcquence of it, the
public has Idfl the benefit of an inftitution,
that for many years promifed the happic((
e^Ss, by encouraging marriage, and affowl-:
ifig relief to indigence. T*he rapid fall of
the intereft of money j their admitting pur-
chafers at too advanced ages j; and, particu-
larly, their paying no regard to the diffe-
rence of age between huibands and their
yrives, muft have contributed much to hurt
them. Some of the principal caufcs, there-
fore, which have rendered them unfuccefe-
fnl, may be now avoided ; and for this rea-
fon I ihould be glad to fee fome fimilar
icheme, providing, as this did, annuities for
lifcy and not for widowhood, undertaken. If
^cll planned, it would, I think, be a propo:
objeft oi parliamentary encouragement.

It murt, however,' 'be remembered, that
the iffiie of the beff fchemes of this' kind
|nuft be in fome degree uncertain. For want
of proper obfervations, it is' not poffible to
determine what allowances ought to be made,
on account of the higher probabilities of life
among females thaA males; No prudence
can pFcvent'all loflcs in the improvement of
pioncy; nor can any care guard againft* the
ihconveniencies to fuch fchemes, which miift
arlfe from thole perfons being moft ready to
^y to them who,' by reafon of cohceaied dif-*'

• . • orders^

«> « - « -

providing Annuitks for Widows. 105

prdfers, feci themfclvcs mpft likely to want
the benefit of them.

The focicties, therefore, on which I have
fcmarkcd in the firft fedtion of this chapter,
would have reafon to take warning from what
JSas happened to the Mercers Company y were
the fdhctiies on which they arc formed per-
fcfily unexceptionable. Rut I have demon-
ftrated that thefc fchemes are very defeftivc;
and that the longer thcv are carried on, the
more mifchief they muft produce. 'Tis vain
(as appears from Qucft. III.) to form fuch
eftabliftiments with the cxpeftation of feeing
ifhcir fate determined foon by experience. If
pot more extravagant than any ignorance can
well make them, they will go on profpc-
roufly for 20 or 30 years ; and, if at ail to-
lerai>le, they may fupport themfelves fbr 50
or 60 years ; and at laft end in diflreis and
ruin. No experiments, therefore, of this
Iprt fhould be tried haftily. An unfuccefsful
experiment muft be produdivc of very per-
nicious efFeds. All inadequate fchemes lay
the foundation of prefent relief on Jufure ca-
lamity, and afford afliflance to zjew by dif-
appoiriting and opprcffing multitudes.

As the perfons who condudt thefc fchemes
pan mean nothing but the advantage of the
public, they ought to liflen to thefe ob&rva-
tions. At prefent their plans arc capable of
being reformed; but they cannot continue
j^ always ; for the gi'eater numb«' of exor-
bitant

ic6 Of Schemes for provuBng

hitant payments they now make to annui*
tantSy the more they confume the property
of future annuitants, and the lefs pradicaUe
a retreat is rendered to a rational and equita*
ble and permanent plan {a). They ihould,
therefore^ immediately {b] either reduce their
fchemes, or change them into one of thofe
v^bicfa I have propofed. But, I am afraid,
this is not to be expeded. The negled with
which they have receivccj ibme remonftrances
that have been already made to them, gives
reaibn to fear, that what has been now faid
will be in vain i and that thofe who are to
come after them, ipud be left to rue the con-
f(^qi)ence& of their miilakes.

SECT. IV.

Of Schemes for prtmHn^ Annuities for Old Age.

A General dii*pofition has lauly fliewn it-
fqjf, to encourage fchemes for grant-
ing (annuities tQ.^tiGMS. in the latter fbges of
lile^; and this ha$ occafioned the 6th Queflion
in the forn^er Chapter; and, as a further
an^d q^QT^ particular diredion in caies of this
kind, 1 have thought a QeceiTary here to give
the foUawing TaWe.

(0) Sm p. $2, 8}. SeA. h

.(^) Thu^i wm ihf £^9dpn Ai\Mwtj Society to. make
tbcir l^weft ani^uity |o/. the next 20L and the highcfft
36A ttiey would probably be fafe. . But, afler proceeding
on ^beir jprcfem phn fome years longer, fuch a redaction
would fry; 00 iM^ns be fiiflcieoc. See » Cariber account
of ^bafeySocieties in the Supplcment.

7 Values

jitmuitifffpr 014 ^^»

IP7

ganJorYiftfZf-

frtfint farmtnt,
fent.

3 ^r ffitf .

19

^-^55

?.oi5 ;

15

J-5»3

2.444

?o

2.023

2.989

25
30

35

^-594

3-369
4-446

3-644

4. coo

5.667

40 1

5-953

7-23*11

.07«9
.106

,146
•203

»?97
.466

.822

^i faymtntt, *ti11

thfi end of » y9kTf Intereft
jAteitil 4 fm€t,\ } fir tnu

• II

« •

.I4(
.193

•259
.366

•559
.950

ValuM of thtl
»fter5S,to«|ei

30
31

419

45

2.114

2.722

5.P88

f Vaiacf ia *iMM>
si {Mjruma tiU
5J-

a'937,
4,708.

.1^57
.241

•394
•703

.297.
.404.
.803 .

■^-r-

■(•^"^K

VahiM of the
fame aoiuitf,
afUr60ytpagef

35
4P

45
5<?

1.667

2-234
3-043
4-255

2.290
2.923

3.3.1 1

[5.061

/Vilifa in tfinii*

'»35
.203

•327
.600

,168

.245

.384
•679

the numbers in the 2d and 34 cojumni
pf this Table, multiplied by any annuity,
Tifi'xW give the value of that annuity ia z Jingle
payment, to be enjoyed for life, by the agtt
porrefpondiog to thofe numbers in the firft
pplumn, after the age mentioned at the head

of

1 oS Of Schemes fir providing

of thaf'column.^ — And in the fame manner j
the numbers in the 4th and 5th columns will
give the values in annual payments.— Thus :
The value of 44/. per annum ^ to be enjoyed
for life, after 50, by a perfon now 40, (ihte-
reft at k per cent.) is 5.95, multiplied by 44,
or /. 261.9, in a ^/z^/^ payment ; and .822,
multipted by 44, or /. 36. 16, in annual pay-,
ments "jtill 50, the firft payment to be made
at the ind of a year.

In order to find the fame values, partly in
annual payments^ and partly in any given en-^
trance or admijjion'money ; fay ; "As the va-
•* *lue oi^i given annuity in ^^ngle payment,
" (found in the way juft mentioned) is to the
giveri entrance-money ,• fo is its value in an^
nual payments, to a fourth proportional ;
^' which, fubtradled from the value in annual
** payments^ the remainder will be the annual
** payment due, over and above the given
«• entrance-money/'

€€
€€

Example,

Suppofe a perfon now 40, to be vi^illing to
pay 200/. entrance-money, bejides fuch an
annual payixient for 10 years as fhall, toge-
ther with his entrance- money, be fufficicnt
to entitle him to a life-annuity of 44/. after
50. What ought the annual payment to be ?

A N-

^Annuities for Old Age* x 09

• ♦

Answer.

jL.8.55. — For, /• 261.9, is to 200/. as
/. 36.16, to /. 27.61 ; which, fubtra<acd from
/. 36.16^ the remainder is /. 8.55.

•

This Table has been calculated from the
probabilities and values of lives in Tables IIL
and VI« The probabilities of life among the
inhabitants of London^ are (as I have often
had occaiion to obferve) much lower than
among the generality of mankind i and the
values in the preceding Table, had they been
given agreeably to the London Obfervations,
would have been lefs. fiut, certainly, tn
office or fociety, that means to be a perma*
nent advantage to the public, ought always
to take higher rather than lower values,
for the ^^ke of rendering itfelf more fecure,
and gaining fome profits to balance lojfes and
expences.

There have lately been eftabllihed, in
London^ feveral focieties for granting fuch
annuities as thofe now mentioned i and he
that will compare their true values, as they
may be learnt from the preceding Table,
with the terms of admiflion into thefe ibcie*
ties, as given in their printed AbftraSs and
^ables^ muft be furprifed and ihocked. They
are all impofitions on the public, proceeding

from

no Gf3tkemes for providing

from ignorance^ and encouraged by credulity
and folly «

It has been flieWri ; that the proper pay-*
tnem, faHowing c^ompound intefeft at 4 pef
cent.) for an antitrify of 44 A to be enjoyed by
a peribn pow 40, for what, may happen to
irertiaJtt ti hni Kftr after 50, i^ 200 A irf ddfnif^
Jhn-m6niy\ htMt^L 8,55, or 8 A i is. in irt-»
ntral payments 'til! ht attains to ^o, the fird
' tjf thefe payments to be rtwdc at the end Off
H year^-^Thc conditions of obtainrng thrs
jlrthtrrty, according' to tb^ Tables of the Lau^
ddhk Shciety ofAnnukdntsfor the Ben^ of age f
wty6L'\ys\ rti admffjim^fhoney \ and 6/. 14^,
iit Annual payments. ^-^htctxHit^^ to the Ta-^
Mey of the foctety of London Anrntitants fof
the benefit ofage^ the condftions (A obtaining^
the faiiie anftftity arfe jo/. in admi^ionrntme^i
and 1 c /. in annual payments. ^-^Thr: KquitaoU
fiotHety of Anntritatits requires for the fame
annuity 38/. 10/. \ti admijjion-money ^ and rj./*
in annual payments. . The true vsjue is, over
itiduhovc^cad/>t^n-Money}n{{ ftiehtioitcd,
itT tenmtai payment of jo /. 17/. (intercf! rccfc-
oftted at 4 /r^r n?*/.) or an ttnnaal payment of
3.6A f5jj (1*^*^^^ reckoned at 'tpert^nt.)--^
The* London Unm Sitietyjbr the cdtrrpsfr table
J\tppatt vf ag^d members promifes an annuity
df ntf left ihan 50 gtwneas for Rfe, after 50^
^ a peribn now 40 for 40 A 10 /• in admif-
Aon-money, and^ *% L in annual payments.

The

AinntUiiisfit OU Agtt ' i r i

, • • •

The Amkakk Society of Annmittmtsfdr the
htnejk of age^ promifes an annuity of l6V. per
MhnufH^ for life^ to a perfon now 40, after at-
taining to 509 for 26 A i6i. in admiffion-mo^
nej^f and 6/. in CTtnual pMyffttnts .^'^Th^ trxx^
value of this annuity is 28/. 1^/. in admif^
Jhn^money^ and 1^/. 8j. in anntiai pavmtnts^
(intereA fuppofed ^i^per cent.) ; or tneifime
fum \n admiffioH'-moneyf atid 20/. i9/. in m*
1%ualtayfnents^ intt rcu fuppofed at '^per cent. '

Tnc Providint Society for the henefii of age
{trooMfes an annuity <A t^L to a perfon now
4O1 after attaining to 50^ for 34. guineas iti
admiflion'^aioney^ and eight guineas in anhu^
a] payinents. The true value is^ 34 guineas
Ui aJmiffion-fnofteyf and 15 A izt. in anfmal
payments^ tntereft at ^per cent. ; ot^ the fame
fum in admijion^moneyf and 1 9 A in annual
payments, intcreft btii^g at 3 per cent. {a).

But I will not tire the reader, by going, lA
this manner^ ihro' thefc^hemes of all thefe fo-
cieties* The contrivers of them, it is ccruin^
can know nothing of the principles on which
the rule in Qoeft. VI. and the demonftration
of it in t^ Appendix is founded ; and, there*
fore> if unwilling to be guided by the autho^
rity of noathematidaftSi it oiay not be poffi^

(a) Tbt account \»xt grvea of tke term* on which a
fterfon wbore age ie 4O, is adiaitted into tbc fe focietrtes, i
have taken from their printed Tables as they ftood at the
cfid of the year 1770.-^111 the joungcr ages, the Aftfici-
encics arc greater.

ble

Hi df Schemes for ptwimri^

ble to convince them of their miilak^s, I
will, however, offer to th^na the following
demonflration, which will be underflood^
without difficulty, by every one who knows
how to compute {a) the increafe,of ntioney
at compound intereili

The value of a life at j^bi (intereft being
at 4 per cent.) is 1 14 years purchafe by Table
Vlfc For an annuity, therefore, (i£^^Lper
annum for life, to be enjoyed by a perfon ai
this age, 498 /• ought to be given* TWd in
tAree of a number of perfons at the age of 32
wiii, (by Tables III, IV, knd V,) liye to 50 a
and therefore, in order to be able to pay an
annuity to them of 44/. for life, after 50^ the
money now advanced by every tJbree^ ought
to be fuch as will, in confequence of bein|^
laid up to be improved, increafe in 1 8 years
to double 498 /. or to 996 /. — ^From the pref
ceding Table it may be learnt, that the mo^
ney which ought to be advanced by every
iingle perfon is 165/. or hy three perfons
49 5 1, and this, in 1 8 years, will double lU
felf, or increafe to juft the fum that will
then be the value of the annuities to be paid^
<-^But the money required in this cafe by th^
Laudable Society ^ is i/^L 11 s. gd. from each
member at admiflion, beiides an annual pay<^
ment of 4 A The admiflion-money^ th^re-^
fore, of two members, being 29 /• 3 j^ 6di

{a) The eafieft method of doing tins, is uught in tl#
rules annexed to the Tables in the Abpendx^c.

may

Jbm)iitiesfir BfJ Agt^ 1 1 3

Itoiy Syt increafcd to twice this fum, ot to
5^/. y s. An annual payment of 4/. for 18
3feats will, if perfedlly improved at ^per cent*
compound intereft, increafe to lot i; and two
Aicfa anoual payments will increafe to 204 A

The whole pay, therefore, of t'Wo mern->-
bcrs will produce at the end of 18 year4
^62 /. 7 j:— A third part, I have faid, will
die without attaining to 50, and thefe will
live one with another 9 years • An annuity
of 4 /• for this time, will produce a capital of
42 /. 6 X ; and this capital improved for nine
yjears more will increafe to 60/. The whold
profit, therefore, from the member who will
die is, his admiflion-money doubled, and
idded to 60 A or 89 /. 3 /• 6 d* And this futA
added to 262/. ys. makes 351/. 10 /• 6d.
the ii>6o/e money with which the fociety can
be provided, at the end of 1 8 years, to bear
the expence of two life-annuities, worth to*
gether 996 /.

By a fijnilar computation it may be found,
that the improvement of money at only 3 p^er
cent. will^iBii the former fum to 3 £4 A at tlM
lame time that the value of the annuities will
be raifedto iioo A

The deficiencies in the ichemes of ttioft
of the other focieties, are no lefs confider**
able (tf)*-^What confufion then muft they

pro-

•

{a) Some of thefe focieties tell us, that the paymenca
QO a4iniflion ihall increafe, as the tiumber of members

I in.

J 1 4 Of Schtj^sfor proviJinji

produce fome time or other ? How barbarous

* • ■" ' •

is it thus to draw money from the public by

ftOr

incrcafes ; nnd thry have praSifed on this rule juft as if
the value of an aonutity was nothing dctermiaaite io itfelf,
but depended on the oumbcr of perfoos who. have beea
purcharcrs. But the true dcFign may perhaps be^ to
quicken the public in their applications.

Should any of theGe focieiies, feofible of their roiftakes^
refolve to reform themfelves, thev ought tpconiider, that
this cannot be done by only obi iging y«//ir^ members tQ
pay thejuft valued of the annuities promifed them. All
the pnjent members muft like wife, befides railing their
payments, make compenfation for what they tiave bt<*
thcrto paid too little ; and this compenfation is to be cal-
culated in the following manner. — ** Find the whole
^* amount to the prcfent time of the payments which have
*' been made. Subtrad this from the whole amount of
*^ the payments which Jbould have been made ; and the
** remainder m\\ be the compenfation required.*'

Example. In the LaudaUs Society- vf Ammhanisy the
condition of a tiik to 44/. fer annum for life, after $0, to
a perfon at the age of 40, was, 4 years ago, 34/. 17/*
in admiffion-money, befides an annual payment of 6/.
14/. 'till he attained to 50. — The admiffion-money will,
( reckoningcompound intereft at 3 per cent. ) amount m four
years to 39/. 4/. an4 the annual payment to 28/. The
whole amount, therefore, of the payments of a member
adniitted 4 years ago, \%i>T L 41.— *But the value of the
aiuitiity was |7 A 4/. in annual payments, befides 34/.
ij s» in admtffion moneys and tbefe payments, during
the 4 years, would have-amounted to 195 /. The 6itk^
rence, therefore, between thefe two amounts, or lay/.'
]<6 X. is the cnnpenfatim which fuch member ought to pay ;
and if he continues a member without paying it, (be--
fides railing his anntui contribution to 37/. 4.^.; he muft
either lofe his annuity, or owe it to injuftice.
** I b^ve taken intereft here at 3 per cent, becaufe I think
thefe focictics cannot reafonably depend on always. im*
proving the money they receive at a higher rate.

Since

'Anniiitiis for Old Agi, 1 1 j

pr6tn1ies of advaatagi^s that cannot be ob-*
tained P Have we not already ixxSettA to0
much by bMks f {a)

I do not, hcfwevttf mean to condemn a!l
iafbtutions of this kind. They may be very
ufefult if the full values are taken^ and pro"
per care is ufed in the improvement of moneys
Intereft, in thefe cafes, ought not to be reck*
oncd higher than 3 per cent, and^ fuppofing
miMiey improved at this rate,* a peribni for a
fingle payment of 50/. before he is 40,^
might be entitled to a life-annuity of 10 gui^
neas after 55; or, if he chufes it, to a life-*
annuity of kjl. after bo. But if he pays the
fame fum before he is 34, he might be enti-«
tied to a life^-anniiity of 14/, after 55, or 22 A
after 60 • %^L might parchaie for him budf
thefe annuities ; and 1 00 A double.

Since I writ the abwe, I have fouad, that the arfnttf*
jlon-moncv required by this ibcietjr has laie)y received
another advance, ^t the age of ss^^ tn particular, it is
advanced to 108 /. 7 /.^^^^when they nave further either ad^
winced the admiffiM^mooey to jinMi fUa (un, or inJpM
the annual payments, they will be timffl rifhc with rdpcA
to this particular age, provided the tm^i^autm SMiary, juft
itfentioned^ has been paid.

TheTe focieties, tho* their pkns art fo infaflideflt, nayt
after beginning their payments to annuitants, coniinuo
them 15, or, perhaps, ao years \ but it will be by 1^*
bijig all the younger members.

\d) See a Arther account of thefe focieties at the end
•F the StrppiEMSNT.

I 2 A fociety

1 1 6 ^ StbtntBs fir ^ovidhtg

A Society or oOke tbftt would go on tka*
plaPA might do great fensioe. Pcrfons in
the lower ilatioas of Ufd Qi^ht he farougibl
to a habit o£ induflry, in the beginning of
life, by ftrtving to i^t .25 A or. ^aL bdbre-
hand ia order to purchaie fuch aim«>iiie$y and
thua to majce piovifiona for thomfeiv^s Jd the
more advanced parts of life^ when thay.will
be incapabjoof {abofif«

There are now eftablKhed in Holland fome
Inftitutions of this kind.-'-^Any poor perfeoa
there^ I atn informedi who can^ before they
attain >ta . a ^rtictil%r a^e^ \»f up . 50 i. may:
make ule or il in bsiyiiig fio^ themfelves. a
right to be admitted^ when 50^ or at any
time afcerWard^^ to hoiife$ ^prepared on pur-
poTe^ for providii)^ them with all t]le con*-
Yeeieociies of lodging aad ho0rd. Thie is ao
excellent i^ftitttUon i . and I yf^(h there wa^
fome imitation of it in thi^ kingdom^

Cbniiderible profks Ivould, in this cafe, be
fet:cired> From the payments of fome who
Vould chufe to delay goiag^ijito fuch houies ^'
and of ofthsrs who would: grow rich enough
to be" above them.

Itif proper to obferve. here^ that inilitu-'
tions of thi( J&ind would furniHi one of the
fofeft ways of providing for widows.-— A mar-
ried man might, by paying 100/. before hid
wife attained to 40, entitle her, after 55/ of
60^ to a life-annuity of 21 /. or 34 /• Or, by

pay-

Annuitiis for Old Age. • 117

^ying the fame futn before (he attained t0
^4^ he might entitle her, after the ftme 4iges,
to a life-annuity of 28 /. or ^4^{a\\ and lA
this caft iie would hsnrd a chance *<rf' iharing

. iHrnfelf in« ihe beneftt'iif the fliNit^. ^

i hate calkdidiis the^^^way^^provkl*
iiig fbri/ridows^ .becaufeacieiKkd-yith none
ertthe dangers arifing frait|\liipit>porti6ii of
dge between men tfiid their stives, ikid from
^ admifiien of pcrft)nrlabotiring:>Ollder con<*

' ' oealed iiiftempers; '

^ 1

1 cannot qoneindft dilia SeAion, without
meniioif iiig the ii^owiAg plan of a ^provifioti
for Old Ag^. '

Let 1 3 guineas be ^iren as etttt^Hce-mofkyi
and let bcudes 1 A a /I 3 A 4A te:«' be given
at the beginning of the firft^ 2d, 3d, 4th, &c.
years, as thft.payments for thefe years refpec-
tively ; aiMl let the laft payment be 16/. at
the beginning of the i6th year. ^A11 thefc
payments put together will, accQ^ding to the
probabiHties of life in the jd^ 4th, and ^th
T^bles^ (intereft being at 4 per cent.) entitle
a peribn, whofe age was 40 when be begun
tmm, to an annuity, after 15 years, •begin-
ning with 15/. and increafing at the rate of
X L every year, 'till jat the end of 15 years

4
t

»

{a) The fame payment before 30, would entitle to an
(Anility of 92 /. after 50.

/ • • I 3 more^

1 1 S OfScbtmesfor fro^)idii^

CDDbre, or {a) when he has Attained to 70, it
bccocDM a itaoding annutcj of 30 /• for tho
remainder of his hfe«

If the addtfion of three guioeas is aiade to
the €ntranip^9mnty\ for every jrear chat any lifo
between 20 and 40 falU fbort of 40, the ta«
hie will be obtained nearly* (^ the fanae an-
nuity to be et^oyed by that life^ after the
&me number of years* and increafing in the
iame tnanoer* 'tilJ^ in 30 years* it becomes
Jlationary and double. — This plan is particuw
larly inviting* as it makes the largeft payments
become dpe* when the 9€ar approach of ihe
annuity renders the encoitrttement to them.
greattji 5 and as* likewife* the annuity i)$ ta
ipcreaie continually with age^ 'till it cornea to
be hi^heft (^)* when hfe is snoft in the do*

cUne*.

*

{a) According to the probabilities of life 10 the Lt^d^m^
Table, thi3 annuity (houlcf be greater,— A T%i$r^m for
finding what the annuity ought to be in cbefe cafes, is
given m the Appendix^ Note (I).

■ *

(i) The lower part of mankind arc objc£ls of p^rti**
eular compaffion, when rendered incapable, by accident,
licknefs, or age, of earning their fubfiftence. . This has
given rife to rnasy v^ry ufeful focieciea amofig them, inx
granting relief to one another, out of little fund^ fupplied
by weeUj contrrbutions. A fociety of this kind, formed
on the following plan, would probably thrive, ^M might,
on fome accounts, be even more ufeful than the inftitu-
tions in Hollani^ mentioned in p. ii6.

Let the fociety, at its firft eftablifliment, conftft of lOQ
peribps^ all between 30 and t^ \ and who(b mean age

WU17

' Annuities for Old Age. 119

eline, sind when therefore it will be moft
Qi«ful.*--It is further a recommendation of
this plan, that lefs depends in it on the im^
provement of money than in moft other
plan€.--^Bat I muft leave theie hints to be
ptrrfued by others. '

may tbtr^forc be reckoned 36 ; and^ let it "be foppofcd to
be always kept up to tbis number, by the admiifign of
new members, between the ages of .30 and 40, as old
fAtoibera( die '6ff. Let the contribution of each member
Isr Amrip^ncc /w veek, oiaking, from the whole body,
an annual contribufion of 85/* 17/. — Let it be further*
Aippofcd,* that feven of them will fall every year into dif-
oTdera, that fhall incapacitate them for (even weeks. —
3p/. laj. of the annual contttbution wiil be juft fuffiei-
eiyrto enable the ibciety to sraNt to eiu^of tbefc I2i«
fir week, during their ilineiTes, And the remaining 55 /,
pir annum^ laid up and carefully improved, at 2xP^^ ^^^^*
"uriit ittcreafe to> a capital that ftall be fufficient, accord-
i^to the chances of life in Tables III, IV, and V, to
enable the fociety to pay to every member, after attaining ,
t6 67. years of age, or upon entering his 68th year, an
anYliiity, beginning with 5 /• ' and increasing at the rate
of A /..every year for feven yeart, 'tJH, at the age of 75,
it came to be a (landing annuity of )a /. for the remain- .
der.of life.

'Were fuch a fociety to make its contribution feven*
pma.per week, an allowance of 15 /. might be made^ on
the fame fuppofitions, to every member during ficknefs ;
beiides the payment of an annuity beginning with 5/.
wlien a member entered hfs 64th ye^r, and increafing for
xj yearf, 'till^ at 79, it became fixed for the remainder of
life at 20 A

If the probabilities of life are lower among the la.bour-
irig poor, than among the generality of mankind, this
plan will be fo much the more fure of fucceeding.

I 4 , S E C T.

tao Of the Amcahle Cttf«fi$thn

S E C T. V.

Of the Amicable SocUtyfor 41 pirpetual AJJu^^
ranee Office : And the Society for Equitable
^uranus vn Lives and Survivorjhifi^

THE <Qth Problem has been given« with
a particular view to ihm corporatioa of

the AmicabU' Society ^ for a perpetual Affu^;
rancc-Office on iingle lives, kept in Serjeant* s^^
Inn. Thi^.fociety was e^abliih^ in 17061^
and is the only one I a(n acquainted with^i
which has flood any confider^lble trial froa\
time and ejcpcriencc. The annui^ paymeai
of each member ufed to be 6/. 41. payablrt
quarterly 1 but it has been lately reduced to
5 L The whole annvial income, hence ariiing^
is equally divided ampngthe moirne^, or h^ir^
of fuch members as die every year ; and this
renders thedividenda amon^ the nominees in
diferent years, more or Jefs, afrcording to the
number of mcmbct*s who have happepcd to '.
die ;n thofe year?. But \ht fbcicty-now en-?,'
gages^ th^tthe dividends fhall not be Je/sthM
150/. to each claim.ant, thougl) they may bd '
itf^rf.-nr-Non? are admitted whofe ages are
greater than 45, or ie/ji th^p iz ; nor is there
any difference of contribution allowed on ac^
Cownt of difference of age,

7 TO<

This focicty has, I doubt not, been trery
u&ful to the public % and ita plan is fucht
th^t it cannot well fail to continue to be io*
It might, however, certainly hav4 been much
more uieful, had it gone from the firft on x
different plan* Jt i^ obvious, that regulating-
the dividends ao&oog the n(^mintis by the.
number of members who die every year, is
not , eqwtabk \ becaufe it makes the benefit
which a meml^er is to receive to depend^'
1}0t on the value of his contribution, but
Qji z, ^ojitinf^epfy 1. . that is, (he number of
x^embers that ihall happen to die the fame
yeai: with him t This regulation muft alfii
Kaye ^leen diiadva^li^eous to the ibciety ; as
wi|l; fippear fr<w> the following account of
the ij^ural progiff^s of the afiairs of fucb a
ibciqfy, when eftabliibed on a right plan.

S^pipofe a tb^ti^md perjbns, whofe comK
mqnt :«ge is 36^ loform tbcmfelves idto a fo«
cif tjf for th(e |«f pp/e of ff/fifrittg a particular
fum at theuf desM^ to Ihch perfons as they
ihaU name, ia copfideration of a particular t
ai|naal-.con$ri^(iQii* to be continued duriog ;
tbc?r lives. &«ppofe ibe.anaital contribution >
t? b^ 5 A . »i)d tbt Itfft paymeiit (a) to be)>

made immediately. Suppoib^ likewiibi the.
o^gi^al nufob^ fifrfbeifocidty )x>he conftantly
k^t up b^ the si^tiijgti df new membersi ^

(ti) Such fzjwtmts^ it h^s been flie^o^ Q^ieft. VIIL^
p.* 28, are better than any halfjczrly or ptarttrly payments,
fild ^t the U^mt time they lave fom^ trouble.

1.24 Of the AmicaiU C^patation

at 36 years of age, in the room of fach as
die.— In Qoeft* X. p; j?, it appear s, that an
aiinuai payment, beginning ifnmediately, of
5A during a life now at the age of 36, ibotitd
entitle, at ^ failure of fuch a life, to 772 L
rsckoiung intereft at 4 ;^i^r cent, and taking-
Mr, Df Mdvris valuation of lives, — A'^Aot--
72ri?i/ pcrfons, all 36- years of age, wiHtJieoff
^ tbc rate of '^to ^vfcry year. The -difB^irfc-
meat$^ therefore, of fuch a fociety will'be^'
the. iirft year, ^otimes 172/. or 344.0/; and
its income' will be 5000/. It will> there-*
fore, at the end of the • year, harb a fttrplus
of. 1560/. to put to intercft.— -In confer
queoce of the yearly accefiions to fupply^ra*
cancies, the number dying annually will be
always increaiing after the fir(k year. In 50
years :it will attain to a maximum; and then^^
the ajSairs of the fociety will become Jiatio^
nary 9 and the 'number dying annually wtllf be
409 and its annual expence will be 6,S8o A-
exceeding the annual c6ntribution, i»88d7. -
But, in the mean time, by improving its fur*
plus monies, it will have raifed a capital
equal to thii^^xcefs, and, confequently, its
affairs will be fixed on a firm bafis foralir
fabfequeat times. , *

Suppofe now, that fuch a fociety, at its
eftablilhment, (Jhould refolve to divide its*
whole yearly income among the nominees of
dcceafcd members. The effeft of this would

be,.

fof: ajfuring Ltves. 12 j

Ttey that no capital* could be raiied ; that the
dkidendd payable to nominees would diminish
continually, ''ttH, at the time that the great«
tft niiinber of members came to die annualfy^
dr« the end of 50 years, they would be re-
dnctd to^halfi and all claimants, after this
period, receive too little, becaufe the firft
4tiairaants had received too much {a).
* At' the time of the inilitution of the ^mi^
eaMe Corporatihn^ the intereft of money was
it '6 per centk and, as they tfdmit all between
1^ and 45, thfe mean age of admiffion can«
not probably be icy great as 36. It appears^
therefore, that had they avoided the prror
now mentioHedf and gone ftom the firil on

(b) The rcrerfis of this will take place, if ftich a fiv
gety itgim with admitting all at all j^ea, and aferwanb

changes its plan, and UmtU the age of admiffion. In this,
cafe, the number of yearly deaths will he greaujl at firft^
and ilie iiviiatdi fiimlUfi. In confeqeence of altering its
pl^. the jearfy ieoAt wiU lefleo gradyaUy, and the £vl-
dendf rife ;, but in time both would return again to their ,
^fginal^attf.

The following Ya£ls incline me to fufpec^, that this
remark may be applicable to the Amicable Corporation.

'" Firft. In their briglnal charUr^ as it is given in their
printed abftrads, there is no limitation of age menti*
oned ; but 31 ' years afterwards, 1 find a bye-law made
againft admitting apy perfon who (bould be above the
a^e of ^5, or under 12. — Secondly. In their printed
advcrtifements in 1770, it is faid, that in 59 years they
h^d paid, among' 3643 claimants, 378>i84/. from
-Whence it follow?, tn^t tbo' the average of their divi« ^
dends, for the laft' j 7 years, has been 1547. the fame ave^-
;agf, for 59 years, is only 104/.

the

• t

x^- Of the AmicMe Corporation

the plan I have ; defcribed ; they might ii^mf
oil along paid to each mminfe lyA L befid^i
rjuiing a capital mMch gr^atefi in bropf^ftioii
to the numjbei^ of rpembefar tJ^aqk .tfiat I hf^
ip^Uiedi by the help' of t^e.exSQei6 of dmr^
:^inual paynacnU. ^bow 5 /. giyt ibmo lather
a4vantageS' ^wjvc^ ^ they h^ve enjoye^ (it),;
Indeed, I qtnnot dou^t but tb4t» wkh tbdb
advaqtagesi tlMry. mighty jbe£or6|this time,
liaye •fout>4 K^i^mieives abl? cp- pay at lituft
zoo /• tO! each 9fOf9iiw^y aad )9fcihe fa;]^ -titow
rf%4<fUd iheicielves^ as theyotiw do> vt/o aa
annual payment of sL{i)^ \ ■ \

• n

[, I have already mentioned cMie inftaiyre int
which the plan of this fociety is not equita^
ble. Another liiiftance of this is, thilif tt«
firing -dio fattte paymeitfts from all pcr-
Ibns under 45, witnout regarding the difFe-^
razees of their * ages ; whereas, the annual
payments of a perfon adAiitted at 45, ought
to be double- the annual payment of a perlba
admitted at 12*

(a) A furplus from a thoufand membert of oviyfioi
filings' per armtm^ duly improred, at 4 fffr (ml. would^;
in 4t years,' produce a capital of 25*000 /• \ .

{b) It ihouU ht remembered^ that all this is faid on
the fuppofitfon, that proper care has been taken to keep
out unhealthy perfens ; and that the probabilities of li&
among the members of this foeiety, are the fame witli
(hpfe in the 3d, 4tb, and 5th Tables, m the ApptnSx.

Further^

f4^ qffurMg Lives. 12j^

* Putther. The plan of this iockty b ib
AirroWy as tt> ooDfioe its u£tfu]nef$ too dnacli*
It cim be of no &rvice to any person whofir
age ^noeeds 45 » It is, likewiie, far from be^
iOg properly adapted to the cirauoiftanctt of
per(pQ8».who want to make aflurances on their
Uves, Jfbr Only (hort teems. of year5«--Tlias %
the true value of the affiirance o£ i^oL £c€
10 yearsy on the life lof a ^^ribn wfaofe age
is. 30, is, byQaeft.XIV«(intereCkbejng.at 3/l«r
UHt.) zL Its* in annual payments, for 10
years, to begm at the end of the iirft year ^
and fubjed to failure when the life fails. But
£jKh an aiTuranee could not be made, in this
ibciety, without an annual payment of ^l.^^
Neither is the plan of this fiiciety at all
adapted to the circumftances of perfons, who
want to make afluraoces on particular £ir-
vivor{lups.'«-<*For example. A perfon pof^
ibfled oi an eftate, or falary, which nuift be
loft with his life, has a perfon dependent
upon him, for whom be dcfires to fscure a
fum of money, p^able at his deacth. But^
he deiires this only. as a proviiion againO: the
danger of his dying^;^, and leaving a wife,
OF a parent, without fupport. In thefe cir-
cumftances, he enters nimfelf into this fo«
ciety ^ and by an annual payment of 5 /. en-
titles his nominti to i co A In a few years,
perhaps, his nominee happens to die^ and,
having then loft the benefit he had in view,
he determines to forfeit his former payments,

and

126 .Of this Society fir

•and to withdtiaw from the fociety. In Oii*
.way» .probably^ this fociety muft have gain-^
cd ibme advantages. But the right method
wottid have been, to have taken from fuch'S
perfon the true value of' the fum aflured#
^' on the fappoJition of non-payment, pro^
^' vided he ibould furvive/' In this way he
ivould have chc^en to contra^ with the Ah
ciety \ and had he done this, he would \kwt
paid for the affurance^ (fuppofing intereft ac
3 per cent, his age 30/ the age of his n^
mime 30, and the probabilities of life as in
the 3d, 4tfa, and 5th Tables) 3/. 8 /• \a) in
annual payments, to begin immediately^ and
to be continued during tht joint continuance

of his own life, and the life.of his notfiinee.

* • . ' *■ ■

' All theie objections are removed by the
plan of the Society kept in Ntcbolas^Lanif
Lombard' Street^ which has juflly ftiled itfelf
the Society for Equitable AJjurances on Lives
and Survivorjbips. This Society, if due care
is taken, may prove a very great public be**
nefit. It was founded, in confe^uence of

■

. (a) The value of 150/. payable ^t the death of a per-
fon» aged 30, provided he furvives another perfon of the
fame age, is, by Quefl. XL Chap. I. 7.45.65 ; and this
value divided by 13.439 (the value increafed by uaitj^
of two joint lives both 30) gives /. 3.4, or 3 i; 8 1.—**
The value of the fame reverfion, according to the pro-
babilities of life In £^Wi0ff, Is, /• 49.19, in 0;«/ payment;
and 4. 16, in annuai payments, during the joint lives, the
firfi payment to be made immediately.

5 F'^

EquitaNe J^urances on Lives. 1 27

pifiQporals which had been made/ and lec-
.turesyxecomcnending fuch a defign^which bad
been read by Mr. D^Jon^ the- author of the
^atk^maiical Repofitory. 1 1 afiiires any foms
or reverfionary annuities on any Isyes, for
any number of years^ ae well as for the whole
continuance of the lives^ at rates fettled by
particular calculation; and in any manner
that may be beft adapted to the views of the
perfons ailbred. That is ; either by making
the afTured fums payable certainly at the fai->
lure of any given lives ; or on condition of far*
vivorfhip; and alfo» either by taking the
price of the aflurance in one prefent psymeMti
or in annual payment Sp during atiyfingleor
joint lives, or any terms lefs than the whole
continuance of the lives. — ^Infhort; the plaii
of this fociety is fo exteniive, and fo impor-*
tant, that I cannot fatisfy my own miiid^
without offering to the gentleqien concerned
in the direction of it, the following obfer*-
vations, hoping they will not thiak them
impertinent or improper.

Firft. They {hould confider what diftreis
would arife from the failure of fuch a fcheme
in any future time i and what dangers there
are, which ought to be carefully guarded
againll in order to fecure fuccefs. I have
already more than once obferved, that thofe
perfons Will be moft for flying to thefe efta-
blifhmcDts, who have feeble conffitutions,

or

J 2 8 Of the Society for

or are fubjec^ tc> diidempers, which they know
render Ith^ir \vfei particularly precarious >
and it is iobe feared, that no caution witl be
fiifficient topt-event oil danger from hence*

Again* In matters of chance, it is impoA
fible to fay, that an unfavourable run of
events will not come, which may hurt the
beft contrived fcheme. The calculations
only determine^probabilities ; and, agreeably
to ^efe, it may be depended on, that events
vrill happen on the whole. But at particu^
iar periods, and in particular inftances, great
deviations will often happen ; and thefe de*
viations, at the commencement of a fcheme,
muft prove either very favourable, or very
unfavourable.

Bat further. The calculations fuppofe,
that all the monies received are put out im^
mediately to accumulate at compound inte^
reft. They.make no allowance for lolTes, of
for any of the expences ^ attending manage-*'
ment. On- thefe accounts/ the payments to
a fociety of this kind, ought to be more
than the cakolattons will warrant. The in-
tereft of money ought to be reckoned low i
and fuch Tables di Obfervation u(ed as give
die bigfaeft values. Mr. Do^fon^ I find, has
paid due attention to all this, by reckoning
interefty in* his calculations for this fociety,
at 3 per cent, and taking the loweft of all the
known probabilities of life, (M* thofe deduced

from

)

Equitable- Affur inch 6n \Live}. ii(^

from the London bills of mortality .(ir). fTharer
i\ bdSdes,* a liberty |3rond^ of making, a
call on all tbd tnernber^^ in ca£i.Dfidiur\ptir--
titular emergency. Jt is^ therefore^ highly^
probable^ tbat this £bcidty (proYided.toQ mach*
money is nbt fpeatia3naoageme;^tVimiilibe'
fccure. The laft expedient^ hoswcvor/ Ytotkl:
be a very difagreedble one^ ihould theKe.be
cyfcr any oceafionfor having recourie;fx) it^
arid^ in order to giurd.ftill. more e^iSlitallyi
againd danger^ it would not,. I think, be amif^
to charge /a profit of 3 or J^fer cat A, on all the
payments .--^Should the .coniibqttence .o£ this
prove, that in fome.fafiut peciod the itiCMtyi
ihall iind itfelf pdiTeilied df ; too large a.capi^
tal, the. harm >yjtU be trtfling, tod. future
members will reap this advstntage. But tbi«
leads me to repeat an obfervation of particu-^
kr cbnfequenQei

- As this fociety is guided in. every inftancej
by. ilriiSt calculation^ it is not to be expe<Sted

(a) It oughti hdwerer, to:be rtmeqibenml fiere; tbM in
lelling life-annuities to commence either immediatelyi^
or after given terms ; and alfo in ibme other cafes, the
values cotnd oiit i^s in confe<)uehcfe of lower probabilities
of Itfe. Would it, in futh inffainces, be tak iilg an unfair
fid vantage, to eftimate the values by the 3d, 4th, or ctb
Table in the Appendix, rather than the LonJ9nTMc r— ^
ThtiS ; was the'fotiety to fell io/. pif" dhmfn^ for life, t<i
fl perfon now 30, aftifi* attaining to 5^, the valuer ac<^
•ording^o Dr. HaHty*% Table, would, r^koniog intereft
at -^per cent, be 90/. in a fingle payment; but, accord^
ing to the London Table, the value woiild bfe only 70 /.

K that

i^o Of the St>ckiy for ;

liiat it tan mett widi any difficultiies i^
many years; bectufc^ YA>t ^dll the end of
many yeart after itiias acquired it^maxinnlm
t£ members, will the m^mnm of yearly cliil*
manta and amiiittaQts cbnie upon it ?' Bheiuld.
% iherefoM» thro^ inattention to this remark^
anid tfafri^DCxrarragement arifitfg frdbi the poT*^
fefiion of a large fbrplus, be led to check oe
fiop fhrincmfe of its ftcck by enkr^^ngits
dividondi^ too ibon> the coniequtnces mig^
|vove pdraiciotts. ' < ' .
' Again* I would obferre, that it is of great
importance to the fa£tty of foch a fociety»
diat iti afikirs ihould be under the infpe6tioo
ef able mathematkims* ' MelMcholy exp^
aience (liews^ that none but mathemadciaba
are qualified for. formitig and condiiding
fchemes of this kind.«^Inihort; dangerous
miftakes may fometimes be committed^ if tho
affairs of fuch a Society are' not managed fru^
gaily, carefully, and prudently. One inftdn^
of this I cannot avoid mentioning.

A pdrfoh, ^ho deiircs to afiure a tiarCku--
lar fum, to be paid at the failure of liis fife,^
on condition of the fiurvivorfhip of another
life, may chufe to pay the value in anfffial
contributions during the continuance of his
pwn fingle life, rather than during the c^^
tinuantce of the joint lives, becaufe the an*«
Dual contributions, in this cafe, ought to bt
much lefs. But a fociety that would prac-
tifc fuch a method of qjfurance v^ould hurt
.•• . itfclft*

«* • •

hfelfi fi>r$ as fddn 48 the life; on whdfe fbe-
Vivorfliip the alTurancfe depends^ is extinft^
the ^Hfoli fiffuiitdi if thdD liTin^, wotild hayci
too lonkcif any beHefit in viei/r ; and; there*
fore} would make his pi^mtots with. reluc-^
tancej and In time; pei;liaps^ pntirdf wit£|«
draw them j thd c6nlequen<^e of wUicn frouM
he^ that the foeiety wodid fuffer a lots of
being deprived bi[ the juft ^alufc ot the ei^
pe<3ati6n it had gi^anted:. Ttie plan of a lb-
dety ought always to be fuch; as that t^
' lofles arifing ftt>m difeonttnuante of paynient;
Aould fall on the ptlrirhafer; and ntier iid
the focicty i

I mtifl Hot iorgtt io add, that it is necef-

iaryj that fuch a fociety fhould bi fuinifl^

ivith as botnpleie a fet of Tables as pofiible^

This ^ill rcftdet the bufinefs of the fociety

tniich mcfte fcafy^ aiid alfo much more capih-

. hie of being condtidtcd by persons unfkilled

in mathibra^tics; It will alio contribute much

to it$ Jafity. For in all cafts to Which Ta^

hies can bfe extended^ there wonld be no oc«

tafion for employing any calculators i indp

tonfequently^ a danger woiild be presented

. 16 whichy tho* it is not noiv, it may b&eaf^

ier be cxpofed ; I mcan^ the danger of Kipr

. pening to truft Unikilfal^ or carelefs calctila*-

, tors.T-^Mr. Dodforij I find, has furhiflied this

« fociety with feme impprtant Tables i and his

jkill was fuch, that there is no reafbn to

- dodbt^ bdt they may be depended 0.1, They

K 2 hare

^dve alfo; others which, Iboliev^, 2ift&^

^fod accnrate^ But th^re are Tome dill wa^^

Jng whi,c^ mould be fupplied j and all (houkd

^be fubje£i<:d to the examination of the be^

.judges^jai^d aftff warden pvbli(hed| together

^Y?ith a uiinute accoyDt of thq prin^'pfes af-

:fumedy and the method taken. in cooipoilng

them; .Such ^, publication would be a valuH

iable addition to this part of fcience^ ^flciJC

.would alfo b^ the means of increailng wd

-cftablifliing the credit of the fociety.

*.' la Qaeftlons 4th> 6tb, joth, iithf i4tb,

15th, and 46th^ I have, with a particular view

to this fociety, given rules, by^which may

be fornicd every Table- it can want, for (licw-

•ine the values of aflurances on the lubole dih-

ration^ or any terms^ of any one qr two lives,

•in all po^ible cafes j and nothing but care

and attention can be neceffary to enable, any

good arithmetician to calculate from them.

Perhaps, this may be as much bufinefs as atiy

one fociety (hould under take« Rules, how*

ever, for finding the values oi .ajfurancei^ in

moft cafes, where the whole duration of any

three lives is concerned, may be found in Mr.

SimpfOTis Seled: Exercifcs, from page 299 to

p. 307; and it is not poflible they ihould

follow a better guide*

CHAP.

I

• "t '1*33 1

* J

m ' • * *■

• * *

C H A, P. III. . «

•• f * r* ' *. •

• •^ w <

• • • 4 '

(SyPuBue Crbmt, and the National

» • • •

rTP^HE NatiQrtal Hcht is afubjcft lA'w^ich
I • the public is deeply intefefted.''*Somc
obftrvations havj& otcurrcd to me upon itj
which I think important ; and for this rear
fon, though foreign to my chief ptirpofe in
this wort, I cannot help here bagging leave
to offer them topubjic attention.

The pradice of raifing the ireceflary fup-
plies for every national fervice, by borrowing
money on intereft, to be cdntinued till the
principal is difchargc^j^muft be in the high-
eft degree detrimcntaf to a kingdom, ttnleft
a plan. is fettled, ;fbr putting \ik debts into ^
regular and certain courle of paymiiii;. Whoa
this is not done; a fclngcjom/tiyfac^fi ft'f)rac-
tice^ obliges itfclf ,ta return^fbf ^ery^ftdh it
"borrows ^infinitely greater firhs ; Wd^ for'th^
fake of a preftnt advantage, fubjed^ itfel/^to
' a burden which ipufl: be always ^Vowitig
lieavier arid heavier, ^till it beCdmeSMnfup-
])l>i-tabic. - -^ i

■ This leenAs to * be/ now thcf very ftate of
this nation. At the Revoli/tion, an sera

K 3 ^ ia

t^^ pf Puhlie Crt£t^

in otjjef rcfpcdis tply glorious, the praSicj;

\ ba« mentioncti' begun. ' Ever firice, the

public ^cbt - Ifi^s bff n -iiinYafiil^ fafl:*' an^

evei^'new waf hw a^dei^'piuch'more'to it,

ithan wa^ taken ffom. it, during tjie preced-

\ng.^ifv)A oF peace. In tiie' fear'i^oo, i^

wasi6 piillions. ^ \n \y\s* ^^^^^5i^}\':

lions.' ^ peace, yt^hich continued tjl] 1740J

jualf;,.it:t0. 47'mUlionsi but ch« fttocee^Bg

)ffzi inqrcaied it .to '^^ ipiMionsj J™i ^^

qext p^ace.iyi^k U op lower than 72191^

iions.*',In ^^ l^'-^^i it rofe'tQ-HS tnalj

|j^n»! ,|P|u^ing a.bcafc Vbich haa laftc^ now

10 yearp^'itivas been reduced to ne^'^j?

ipillions ': Aod at a fupfi not oiuch le& than

this, it will, perbaps, Ibe found at the com-

ipencctpcnt '<if mother war,, which may pof-

'^Xy rai(^ it- to 200 niiUicins.--Onc, cannot

;|c^q<|^'on' tji^s >?^iHop t terror.— 1;"^9, rcfomces

can ij^ fpftci^ot, io ,%|pcift a jtjngdp.tTi Ipp^g

]n iuch a, Cfliiric;. , ,' *'^'ii. obvious, ''fhat dftt

cpore^uen^ f^ ac'cujxiuUttn^ debts {9 rapid-

Iva ftiid i^mprtgagipg'.^pfteritx,' antj.'fund-

otcfnitjrt'm' order p^ paj]thp,iqt?rfi4

i ffH"i(B f'^'^S^ prove '(fc^uOivc^

tbah.go 911 iA tbis w^y» '|t^^ fK^r

toce^ry, tfiai j^o isooey ihquid be

;dj txce^jk onf!ai^4itie«,' *flyiph. ttre

linate wif|iJia,3^ixen,period. -, Weri)

aired, there wou1<f be a tiMfcl^ite'r

yowfvhich ^phsiion^jdf^tsjcop^d.ijftfcin-

crcaie'; dQJ.tiqie w(Hi£d do.that nt^^^T^,

f^ tb« public^ vthicK» if tirufted to tfa* qmo«*
j|rOfny of the .<dadvM39n;o£ its tffiirB; might

.T|ti)9> tbendfbrt, i». One of the propofirfs t»
ly^c^ <A^ thie [o^cfafion* I wi£h 1 <x^d en-*

5age.9flei)Cion.-»I am ftfifible^ indeed, that^
be pt^ftnt burdens of the ftafe woaidj in this
9i&%9 ^ be ifiQrfc«i!ih}^ ia confeqtieiKe of th«
^ftt^W prefeot ilurqOif chat would be necer«»
fucfX^ be given for tnoo^. :B<tt I do nof
oQnfider this ^ aa dbjedion of any weight*
Jr or let tbe aaouitj be in annuitjr for a lOo
years* Such an amloi^ iv to 'the pceiimt -
yiewf of oien, iiearly the iame)With aa tnaul^^
fy/fpf f ver I and it ia atfo nearly the 6me in
calcuktioo^ ita >valiie at 4 per cmt. being
ti4T years purchafet ^d thecdbre ooly half a
year's purchase lefa than the value of a pen^
P^ttfity. Suppofiag, therefore, the public, able
to borrow money at 4 per cent, ca tntiuitiea
lor $ver, it ought ooK to give above i $. yd.
per, eent. moK formoocy borrtywedooaonui^
ti^s for J 00 yeart z 9at fliould.it be obliged to
give zquartert or even wi hamper cknt^ »oire(tf )^
ihli ftdditiood bwdena dori^ed from heace^

wouW

Ytf) Tlieie an^uitfei Viglit W kept iS pkn wtthMt
beihg'aiwbh dimlaifVed ih value \ tdi^ fuppofin^'intercft
at ^fer cm. an annnjtv for 82 years^ iiy within a 49111

pan; of %L ia ^L wm at amdi at an aMtititj m %
leoyeaif.

' Perhaps, in ihit way oF raifine money,! it mi^ht be beft
tf 9lStt a higher intacft at firft, wfafco ftouM fail to a

K 4 lowtrt

wMiid2k)et>e'-ilich tt<«b«il^ bd very ft^&Mj^
felt) and^tlte ^vantagec^ arifing fr^m tiM
neccflary annihilation of tW public d^bts bjr
timcl>^ t^til^'fltbuhdafltly overbalance them.

i. Tbeic 'afivatitagest would be^ indeed^ im<v
fpedkably^greati ' By fuch a ntethod of raifing
tnbney^ : ihe ^eji^|>ehcd^^f - one "war would, M
tfhie, come^^tp be always di£t:barged/ before
a^new wiii comm&ndbdr9^iid< it would be Iffi;
{Kiffiblc} )A£it a.^^ten^mtld^tver have u{jMi
iti:;9t nn^-oae itime,. the expence of 'ttianj^

waif s4 wi2F(jyJar^r ^bt6 \)Am ^oxkYA,* b6tc^>tar-

traito^ withfit &e limted f^riod of tb^^iti'*
nuicm cuofid/zdOfiiequbitly, - it would * enjoy
die hiiiaddib(btpcivilege^ bf I being I'etidereld;
iniiibibe'/ie^roey; i|idepeMlk^t «f^th4 maA4^e<-
mebtlofiitt finames by ignorant or unfaith^H
ietVl|ntsJ{ > ofil / '^1'= r : <. i ^ .

c!4oi«&(fr:qdtf^ thvt it 2&:by no tntans* qecef-.
&iiyittfaK die •Nmited^'pisriodiirftthe anritittiM
ikipld ibe fift'^long aia I haKrt.meiltioned, or
)-b0:3iiitaflr&i)JliiMi:that| :>ooatiy ti^^ tiie

Ctpbi|Hdo»fitttis: p^k>di ^tfa^'^piibiic'^cniigbt
((npioyraa^&rpiiis £iQOAtt;$/m' ex<iAgUi(hif]f|^
pourecs ihej^iKiiftieSy b3r|teMAaring4he»i f^
iif^lf ."at the market price ; and thus it mighf
aid the operations of time, aod keep it^^ebts
W]tj)i|i arjy Sj^d'ijicfs^'if^iat J^^^ ijitprirft jcn^erj^-

k\"' f .. :. / ^.i ^-..ir.j; . ' sA •*• •• .11; : . ,: .^ ^ *'•

]«wor, «ti;k» je«i •£ giveir istcfraltv vTjiub^ ibb^ 4/ <^r

IOC years ]$ equal in value to 5 ptr ant. for i7 yeapqi^ Mid
jjfterthat.4^rr.r^«/. for Sj.vcars, ycrtliejatccr.fliight
appear mprp ihViW-/ ' ', " .

and tire Nafibnai Hibt. lyjf

#eteilkfy. * Our goVer nment has, I fchaw, iii
«^bme inftancesL adopted the plan now propof^
ttdj'-but It is to- be VrifhcJthati Iriftcad of
TetiafKng in) it, 'as was once done, it had
■fje^iPeapried mdch further, • • ' /
;*• I'atti, ho<^eV4iS far from intcrtdthg to re-
{^thnmend this plan as^ the feeft a ftatecan
^rAie. ■ There-is iribthcr nSerfiod of gaining
^tfac ikme ^xl> which is, on-many acctmntsi
f tenable to it. • I ttitsan, •* by proviiding atl
-^^annttal fa^ng, to -be apphcd invariabl}!^
^ together with the intcr^^6f•aH the fum$
^< rtdeemed by it, tothc parpofedf difchargi
^* «^ the pubtte 'debts : *Or,' ih' other words,
f* by the efl:abliflitoe«t.of a permanent ^ink^

*' lU'd FUNDi" '. ' . • . • '

* ' lf4*'WeM known; that thfs'^ilafi' has been
Hlfo 4Kfopted hy^ 6%^ ^overnmentyf but, • tKb^
capable' bf pf ^iducifiig the ^great^ effcds in
mn^^ebjir/i aod^^^f^Sf maniter, it has nfever
bccft ^rricd ittt^ execution'. *• ^\t vHff abund-
untly appear fv6m what* follows, that this
pbfervation is-jAil^ • * ''

Suppofe^he annual' faving- to be'i 00,000 li
This fum, applied now to difcharge an equil)
dfebt, bfcaring intereft at 4 per cent i wHl trahf4
ii^r to the public, frorh its creditersi'an an-*

(0)\ixk the year 17M, the ftation was put to the exr
pence of above three millions, in order to reduce feveral
{png^^nd ihon annv^ities t^^p fubliAijig, ta r«}<9enMt>Ie

nuity

^^38 qfFubUc Credit, .

puity of ;4»ooo/. At.jt^ cod of a y^ip^
iji^q, thfrc would be a (ayipg of i<?4,Oftoi
iwl^ich wpuki tqinsfcr to, thf piublic aao(^
annuity of 4*160/. aad^^ake thc^fa^^l^i $^
the end of two years, to; be ^o^yi^o/^^rt'
!!^kus, the origmfd fund would go on inci^afr
ing,. at the faoje rat^ wit^; mopey i^pciAv^
at 4 j6^ or^/. coifippund intereft; — :At.ilbf
endof thre^ycarsit wpuldilje 112,48^/4 -JA*
jilhe end of 1 K ycars^'aoajsS i A: Of ^4 3!»f%
^t 0^393/. ^<^d.9f 95 y^a^*^ l^)^ 4# i 5 u i^a^^--*^

^t the endof 93 years, tlvffi, ^He nation I9f^gkc

jbe ca£bd of above 49UJUiQn« j^Fr.4iMM«l ift
t^xe$; ^ind. abpye .loq fnUUons of Us 4#bti
Syould be di&harged, gta4¥^Hy anjd infec^^ly^
at no greater expcncc than ioo,oooy, ft^.^n^
pum; a^dy wi^i^ut h^terlci^ifig vith.49]r of
i^ refourcesr lOf govemmcn tl or mak4(^ 4f1x
ptherdiffer«9se, tlm ci|niiiitg/«ff^
gaged for a courfc of tia\e to tht puNic% ^hkfh
wp4^1d hsiye bf en othcrwiic. oecjsiSirily c^gvgr
pd to it$ cridUors, ^^4 ivhicbj th^refoff ^ ftwift
have been entirely ufelefs t^. it. / ; : jjr, »
It is an obfervation that deferves particular
attention here, that, op:thw pl«A» it i«^iU:be
of lefs importance ,to a ftate; wh^t iql^roOi it
i^ oMig?4 to give fof m^t^ •■ For jh«,JHghc»
i^ intereft^ the fop^er will fuch a fctpdjpAJt
pff the principal. Thus; a 109 millions
borrowed: 4t 8 flefr eent. and bearlslfi;'^ an*

«

(^ Sm the Qiieftionfs annexed to the T^ble^ hi the

Appendix. . .

and tbt National Debt. , 139

una] intereft of eight millions^ would be paid
€Shy a fandy producing annually ioo»ooo/.
in 56 years ; that is, in 39 years lefs time»
than if the fame money had been borrowed
St ^per cent. {a).

It follows from hence, that reductions of
intereft would, on this plan, be no great ad*
vantage to a ftate. They would, indeed,
lighten its prefent burdens ; but this advan-
Jlage would be, in fome meafure, balanced

. ^{a^ .What 19 here faid, fuppofes thtfame fund applied
to tne difcharge of debts bearing different interefis. If
different funds are applied, bearing to one another the
ftme propoKion with the tnterefts of the debcs which
they are to difcharge, the benefit derived from borrow**
ing on lower rather than higher interefts, will be reduced
to almoft nothing ; for the difburfements of the public
en account of all equal loans, will, in this cafe, be very
Marly the fivM.

The following example will explain and demonfirate
this:

IiCt a miHion be borrowed at ^per cent, and kt a fund
be charged with it, bringing \n fix fi>iUif^s per cent, per amt*
ifioic than the intereft ; or 33,000 /• inftead of ^o^ooo /•
per onn* This furplus, unalienablj applied, together witb
all the interefts diiengaged by it, will annihilate the^rm*
eipaL in 81 years, as may be gathered from Queftion V.
in the Jppendix. And the difburfements, on account of
the loan, will be 8i multiplied by 33,000/. that is,
2.673,000 /. Let us fuppofe again, a million borrowed
at 6 per cent, and let a fund be charged with it, pro-
ducing a furplus of twelve ftnWngs per cent, per ann. fuch a
fund, befides paying the intereft, will difcharge the^/;i-
dpal in 41 years ; and the difburfements, on account of
the loan, will be 66,000 /• multiplied by 41 ; that is,
2.706,000/. or nearly the fame ^ with the difburfements
#n account of an equal loan at 3 per cent.

by

I40 OfPuUic Credit, ^

by the addition which would be madtt to itc^
future burdens^ in confequenc« of the longer
time^ during which it would be Aec^iTary to
bear them. — I meaa this on the iuppoikiotf,
that the favings produced by Fcdw^iQds ^
intereft^ are immediately applied to the re-
lief of the ftate, by annihilating taxes aqui^
valent to them. But if that is not the cafe ^
and if, Hkewife^ there is either 90 plan e(U^
bli(hed for putting the public debts into k
certain courfe of payment, or it is not faith-
fully carried into execution; in thefe 'dr*
cumflaacesy redudions of iaterefl; may prQVQ
hurtful. For^ firft. They vould only im^
Jii{h with more money for fupplying the de-
ficiencies arifing from profufion and ba4
management. And, iiecondly* A3* in iAicb .
circumftanccs, they would only retard, ztA
not prevent the incrcafe of the burdens o(;ca,n
fiooed by the public debts» a p«r>Q4 wog^d
come when the affairs of the ilate would'
get to a crtfis ; and at fuch a period, its dan-
ger would be increafed, in proportion to tl^c^
reductions of intereft that had been made.

In order to underftand this ; let us fuppoie
that a debt, bearing an annual intereft of five,
millions, is the whole debt, which a ftate:
can bear without being fo rnqch oppreft as
to be near finking. Let it, however, be fup-
pofed to h$Lve ftill fome laft refources left*,
which may enable it to bear, for 2 3 years t^-
come, this load, together with every addi-
tional

A»i thtffaiUnaL "Mt. i4t

tiooal loadf which, 'during this tin^c^ may he
ntccfecy .to be. dirown upon it.-^— Let it fur-*
ther be fuppofed, that at this time, the ftate^
urged by the f^at of an approaching bank-»
ruptcyi re^blves. upon entering into foma
effectual tiK^flirca for prefervihg itfelf.— ^
Certain it i9> that in fach circumftances, no
meafure j^ ei&Aual can be purfued, as the
WlabUfhinent of a Jinking fundi and fuch a
faithful application of it as I have explainedi
Let that, then be the meafure entered upon i
and let the ftate be fuppofed capable of pro***
viding a fund, pbodocing a milUon annually/
If all the debts be^ intereft at 6 per cent.
this fund nrould pay off three-fifths of them^
within the time I have mentioned i or, in 23
years;- and' the ftate might be faved. But
if, in confirquence of redu£tions» they bear
intereft at no more than 3 per cent, the fame
fund-would not give the fame relief, in lefs
ih^^d9uble that time; and, therefore, a ban-*
kniptcy* might prove unavoidable^

I wi(h*I could think, that there is nothing
in this reprefentation^ that can be applied to
tbe.jprefent ftate of this nation 4 The intereft
of the* public debts has been reduced, at dif-«
ferent periods, from 6 to 5, from 5 to 4^
and from 4 to 3 per cent. ; but ftill they
have grown with rapidity ; and we now fee
ourfelves overloaded, and in no way of gain-*
ing relief. Had there been no red unions of
intereft, we ftiould, indeed, have been in the

7 iaroc

fimie ^ondftibfi {6ontr ; biiti - ^e dilgiil lnaM
been relkired fllib feoder^ aiid widi 'jbft4Bl^
ficohy aftd daitger.' . t

in' diorr.' Rodttdioms of ihtcxfeA^ lie «i|a
vantftgeoas chiefly when tntdt^ to gaiO' id^
dittons to foch a Jinking fitni as I m? e d«^
icribed.^^Wben made with other vkwi> tfafgf ,
are cnXy fal&ititxi which gi?e prtpfnt nUani
by increafing y^/tfr^ danger^ or exfnBmti
which poftpone a puUic bankropKyi W ren«
derine ^t a calamity morft un4MM4klt ai}d
dtio^l: As ^ managed tharefMiEfi ttiioog
ttSy diey bare been indeed the efFe^ of -too
narrow a p6iicv, and deftrve none di the
Miri^ximMVi whicn have been beftowed yfMNi
tiiem.^-'^^-^The preceding obfcrvatiOa9?prOv^
this fufiiciently I but there is^ orito ibrtliet^
proof of It. which I cannot help oMttftonangi
«*^9uppofe aoo^ooo A per ann% to have beeii
gainMi in ijxb^ by the reduAion whtefa wai
th^n made of the 6 per tents: to $p€r€eM$i
ofj in other words^ by facing i per centi pei^
emnl on a capital of ao milltons# This Mv-'
idg, in confequence of bei<kg applied <iff<(
aiienably in the manner Ibave r€{>reftscedi
to the pajrment of the public debcsi wdfcldf
in 37 years, havt difchargod a debt of
50-325,000/. bearing 5 per^eent* iof^nefti
i^ut if applied every year to current fervioesi
in order to avoid levying new money, thd
benefit derived from it in* the fame period^
wtmld be 37 times aoo^ooo h or /.^ooiooo/i
^ . but

and- tie jSfaiiottdl ttdt, 1^

' btit Vi the ftme time, a debt would faftvfar
heen 'OHvikimd of ao. million^^ which muft:
hzrc been othefwife paid. Tbt^fk&^ ther^^
idtty in this? c^> • 4^* the redodi6iTft wookl
b« to prevent n incumbrance on the public,
^ doOyCecV. /ifr iMir. by leaiviag upon it «v
lHeumbrance*l3f >a miUion per^mn^ rendered
more diflkmlt and unlikely than ever to bp
Yemoiwd.

But to return to the fabjedt I ham priaci««
pttllyin%idw«'

What I have faid imi^iea^ that a ftate il^
Ways dtfcharges its debts, whatever inteidS
they bear, by paying the original Aim bor««
rc^wed. It may, perhaps, be imagined^ that
when a loan is umier par, it may be difcharg^
ed afa left expenee. But this is by nbtneaaa
ib praAicable as it may feera ; for it ibould
be confidered, diat a public loan, now under
fdr, would, not long keep fo, afi^r being put
ifW^ a courfe of payment : And, for this rea-^
fon, as a ilafe can never be obliged, in re«
dcteitting its debts, to pay MM^'e than the ori--
^n«l fum borrowed, &} ncMier ought it to
4mpe€t, in general^ to be able to redcenvdiem
by paying /e/s* I have 'faid, m g^nerai; for
I am fenfible, that at the beginning of the
operations of a fund, when its produce is
fmall 5 and alfo, in a time of war, a ftate
might derive great advantages from the low
price of its dcbt9# And I am^ icnfible alfi>^

that

^1^, ydf Public Creiki

tfuit cohfidcrabtb advantages . mlgbt l» dc^
txired ixomJotteries {a)f in paying the piiblkf
dd}ts : But lotteries/ do great mifcbief inr^
ftate, by.ibftcring dbc \dcftru€tive fpiirit o#
ganging. It is wretched, policy to nyikef
^m ianuliar» by recurring to them in jho
ordinary caurfc of government. There arcf
great; occafions. oa which they miy be ne-**
ceiTary, and for inch occafions th^y 0)Q¥iM
biirefin-vedi. I

The advantages of* patting . the ptiblic'
debts into fuch . a couf 1^ of j payment ' as 1
haye defcribed, are jRrarcely to be im^m'*
cd. . It would give a -vigour to public cre-^
dit,: which would enable a ftate always to
borrow money eafily, and on the bcft terotsi
And the encouragement to lender^ might'
be always improved, without any ancoiivc-*
nience^ by making every loan irrtddsmable^
' during the firft 20 or 30 years; for, t^rc
could feldom be any occaiion^ for beginning
tct. difcharge any Me loan iboner4

It might be eafily ihewn, that the faithful
application, from the beginning of the year
1700, of only 200,000/. annually, would
long before this time, notwithAanding the

(«) Thus ; 800,000 /. of the 3 per €enU. at 87 ; or
1,000,000, at 70, might be pedeemecl with half a million
of moneys confifting of '50,060 lotterj' tickets at 10/.
each, real value ; but capable of being fold at 14 /. as
was done in fome of the laft lotteries.

reduc*

Hidiidions of intcreft, have caufed^ abo\fe
half the public funds to fevert tb tHe
public, and paid off above 80 rAillioris cf
its debts. The nati'Oil might,- thtrefore^
{omt ycaf-s ago, have been ca[fed of the greaf-
ieft part of the taxes with u^hich it is load"-*
cd. The moft important iielief rhighlf hav*c
been given td its trade and manufaAufes ^
and it might now havd becil in much bettdr
circumftancesi tHan'at.the beginrting. of th'c
lai^vfat) its credit firm j refpfffted by fo-
reign rtations ; di*eadcd by its eriemieS ; ahd
.ready to punifti any infuU that cbuld 'be of-
•fcfed to it. The near view, likewlfc, bf fucjh
if period, during the courfc of thfe laft waf>
would have given higher fpirks t<^ the na-
tion, and encouraged it to bear thfe expe Ace
bccafioned by the ^^'ar with mot€ ithearfuK
nefs, and to continue it with vigour, for two
"pr three yeai*s longer.; the cOnfcqueiice of
Avhich would, probablv, have been, gaining
a full indemnification from our bnemies^ and
\voakcning them to fuch a degree, as would
have given us effcdtual fecurity agsduft then!
for many years to come.-^A n/ew account
JTUght alj(b now have been begun ; and an**
other fund^ not much more coniidarable^ ap-^
pH^d in the fame way^ Wouldi in 60 0^70 year*
more^ have paid, not duly all that; \vouI4
have be^.npw um^i^^ butalfo/ probably^
a great proportion of fuch furrher debts m

L moft

146 GfPul^lic Credit,

ttvoSt be CQP trailed wkhin this time {a)^. And
thusi withput -any wpencc that could be fcn-
fibly ff It^ its debtSi as foon as they began ip
;row heavy^ might have been conftandy «-
luccd to a '^aiff ox a third 1 and not only 2JI
danger f bu< all coi^fidcrable inconvenifnce frooi
them prevented.

AD tiiave ppw faid, fuppofes zji^le£\xnd
with a 'genera^ appropriatioa to the payment
of the public dfbts- . TfiG lame cnes migl^t
b« aiifwered by particular fuqds> with iinall
furplufles, appropriated to particular debts.
In the wars of VMk^WtUiam and CL^Annfif
6 per cent^ intcreft Wai given for alt loafls*
It woul4 .h^ve teen c?fy to have jmaeTied tp
caph Ipan ^fwd producing ^/wplw pf tL
per cent* after Myiog the intereft^ and iu^fea
/wrplUs wPtfld nave be?n fufficient ta.anniiii-
Jate th€ principal of every loan in .33 yearsu
Had this phn been followed, the difengfge-
in?nt of ;tne public funds,; and the relief at-
tending \u would have begun 50 years; m[o ^
and the debts contra^od, during the xtxff»
\)(KiitzJf^iJliam and Q^ecajinru:, vrouUl have
been au cancelled near zp years ago^ withont

faj Otic'otrYa (n-opcreft objeds of wxiirori iri a ftate
is ciltltdifi \l iloite ft(fty ^1 tiiat b]^ a fttn4«ft4>ptied oulf
^om ^epci^ the «i}d I b?v^ in view np^^ht ihif^ve htKf
f aOJy ^c^mDli{b€<J ; apd, CQ;iftauQntIy, th^ very rocgn>
Of t>,ay(ng off the debc§ of th6 nation, rendered at the
iadrt'tiili^^eitmafia e(! iA4t««j|ng' it^ chief ftreitgi}), by

f .. .: .:i any

7

tind tie tfationai Deit^ 1 47

any of that traiibki tumult, and diftrefi, which
have been occafioned by rcdudions of inti^reft^
and by the various fchemes which have been
Med for leffening the debts (tf).-^A fund^
yielding i /. ftr cent, furplus,. annexed to a
loan at 5 per cent^ would difcbarge the prin-^
tipal in 37 years {h). At 4 per tent^ in 41
years. At 3 per tenty in 47 years v

Thefe obferratiohs rdate only to What
might have been the ftate of the nation with
refpeft to its debts^ had a right {^lan been
purfued from the firft. But it will be afked^
IVbat can be done with them as they are f-^
I wiih I was able to give a mdre.&tisfadtory
i;inrwer to this enquiry^ ISL^crf one muft fee
XAk 'profpeft tb be difcoaraging, and our ftate
h^drdoGs. Spme have thoogfat^ that a good
ought be found out of diicharging

. (a). The Aints t^ \^ Ifiid ^nK i^wMi in ^\% qpfe^.be i^
rmall at firft, that it wpuld be proper to emjploy them id
purchaiiog part of the loan to be annihilated at the prices
in the public inarket \ and this,- as fer as it ean be car-
Ued^ is the meft eafjr and quiet and fileat ynaj po&bife
tof exiinguiihing the pubKc debtsi

(^) I havr nil along fiippofed the produce bf the pub<«
lie funds to coitie*in yearly. The truth is, that it comes
in half-yeosXy % but this gives no advantage \fi the pay<*
htent of the public debt^ worth taking ibto account, i A
p& Mtautmj together with its gtowing int<reft» at 4 ^
^ifiif tstken fi<irh ovit of 100/. will reduce it to hothing
JQ 41 years ; if taken half-yearly^ it will annihilate the
ikme capital only four months and il days fopner. $ee
thcQaeftions annexed to the Tables in tht jppiwlix.

La the

148 . Of Pulf lie Credit; .

the natibnd debt, by life kanuitics. The fol^.
lowing ob&rvations will fticiv: how vain ari
imaginatibn this is. * v

, Let us fuppofe, that 3r3»?33>o'oo/. fs to
be paid off, by offering to the /public cre-
ditors life^^annukies, in lieu of their "7, per
cents. A life^t 60, fuppofing intereft at 3-J
per cent., .diTsd the probabiHties* of life as in
the Brejlawy Nornjcicby and Northampton Ta-
bles' of -Ob fervation, is worth '9' years pur- .
chafe. A iifc at 30 is worth 15^ years piir-
chafe. Certainly, therefore, no fcheme of
this kind Would be fufiicientiy imriting, which
did not offer 8 per cent, tit an average, to aM
fubfcribers. . Let ik, however, foppofe, that
no naore th^ni 74 is given ; and that there are
33333 fi^bicribcrs, at 1000 A ftock each, for
which a Hfe^annuity is to be* granted of 75 A
or, for tkej whole flock ftibfcribcd, t^omil*
lions and a half. A million and a half ex-
tradrdinaiy^ therefore, muft' be prbvided
every year; tpwards pajang thefe annuities.

Let us J farther fuppofe that the fubfcri-
bers are perfons between *the ages of 30 and
60 J and that the numbers of them, at all
the iiitermediate ages, are in' the fanid pro-
portions to 'one another, with the proportions
of .the. Jiving at tbefe age^, as they exift in
the world^ or, as they are given in Taiksof
'Ohfervdtidri. Let lis again fuppofe, thhtas '
^thcfe animitants die off, thicy are immediately
replaced by aiihcT?, who are- continually otr

fering

end the National Deit^ 149

fcfing thcmfelv^s at the fame iages, and in
the fame proportional numbers at thefe ages,
with thofe of the orieinal fubfcribers at the
lime they fiibferiBed ; in confequencc of
which, the whole number of annuitants will
be kept always the fame. In thefe circum-
f^ances, it will be 30 years, at Icaft, before a
number will die off {a), equal to the whole
mambelr; that is, before 33 millions of debts
will be annihilated. But had the extraordinary
million and half provided for paying thefe
annuities, been employed during this time, in
paying off fo much of the debt at par every
ycar> extinguifhing at the fame time every year
an equivalent tax, 45 millions would have
been paid. But had the favings, alfo, in«
flead of being funk as they arofe, been em«-
ployed in the fame manner, 71 millions
would have been paid. , . . ,

The nation, therefpre, muft, without doubts
lofe greatly by all fchemes of this kind;
and yet they have been often much talked
of; and} indeed^ I ihall not wonder^ (hould^
I hereafter fee an attempt made to pay off
the national debt in this way.

I muff beg leave to detain the reader here
fome time longer. A more particular ex-
planation of this fubje<£t, will lead to fome
obfervations on the beft methods of raifing

(47) A demonftration of this will be given in the Ap«
pcpdix, i)ote (K}.' >

L 3 money

^S^ . O/PuiUc Credit^

iponey which, I ^iiikji ^cifijfyc to be car^
fully confidered* »

When apy fum i; faid to be the wi^o^i^
l}fe-annuity, the meaning \$, that, in confe^^
quence pf being improved at intereil^ ancl'
allowing for the chances pf inortalityj, it wilt
bi?ar the yvhole e?cpence of ihp annuity. lf|j.
th^efore^ inflead pf being /aid up for im^
prqvement;, it is either iihmediately applied
to.part^iilar ufes, or has been long fince fpent;
^Jifire will be a lofs^ equal to th^ fv;m whicli
woul4 have been added to the purchafe-nno-
ney, ha^ it been improved'rr'This i$ the rea-j
fop pf the lofs which J 1 haye (hewHi the pub«^
lip wou^id fuffipr by offering l^C'^annuitm^ in
jjicju ofji^c^, in order to ejltinguiih its debts*
j^nd fp^ the fape reaipn^ it muA always lofe
coniiderably by raij^ng mo^ey on lile-Annuit

Suppofe 4 million raifed. by apnpkicf oa »
f<jt pf liyes, all at 30 years of age* Ferfons.
at thi| age haye, (according tp Table? Hit
IV,, ainid V,) an expe&athii c«^ 28 years. That
IS ; the duration of their liveSj taik^ng them
one ^ith anotherj will bf? $8 ytars j (fee the
beginning of |h« iirft Eflay) alni they will be
entitled, fuppbfing inteMft at 4. pr ctwti to
7/. per annutfis for every iqo/. jwlvanced. For',
a mfllipn then, the public would make 28 pay-
ments of 7o,oco/*-rrT-Let U8 foppOfeheit, tlntt
a fund producing th;s fum annually, inftead
'■ ' "" " ' "'" -^ ' ' of

\

and the National Debt. '5^

of being engaged to pay thcfe life-annuities,
is engaged for 28 years, to pay the principal
and intereft of a million, borrowed on redeem*'
#^/f perpetuities, at 4^^rr^;?/.TherewiU,at the
end of thefirft year, be a furplus of jo,ooo/.—
• In confequence of applying this to the ex-
tindion of the principal, it will be reduced to
970,000/. on which, at the end of the fe7.
cond year, the intereft due will be 38,800/.
There will, therefore, be a faving of 1200/.
Inftead of employing this faving in further
finking the ^r/fza)^^/, .which would caufe the
fund to accumulate in the fame manner with
money at compound intereft, let it be taken
and employed in any other way : And let the
fatne be done with all the fubfequent favings^
rcferving only 30,000/. annually, for the pur-
pofeof finking theprincipaL At the end of the
iecond yegr, the principal will be 940,000 /. 1
&nd the faving of intereft upon it, at the end of
the thixd year, 2400/. At the end of the 28th

?iar» the principal will be reduced to i6o,ooo/*
he faving of intereft that year will be, 1 200A
multiplied by 27, or 32,400 ; and the fum of
all the favings will be 4 5 3 ,6co /.— Dedu<3: from
hence i6o;coo/. remaining then undifcharg-
ed of the principal i and 293,600/. will Be
the lofs X^ public would fuftain, in the cir<*
cumftance^ I have fuppofed, by raifing mo-
hey on life-annuities^ But if we fuppofe
th.c favings, as they ari£e, as well as the con«
ftant fum of 36^000 A to be applied to thte

L4 dif-

ij[2 .Of. Public Cre£t^

difcharge of the principal, jnftead of .bgiri^
fpent bn current fervic^s ; the whole rnillioii
will be annihilated in 21 years and a half; anq
th^ lofs to tl^e public by life-annuities, vvil!
be 6t years . purchafe of the a^inuities ; or
455,O0P/.rr^By fimil^r dedudions it may b^
cafxly found, that the lofs, \u younger lives, i^
greater \ in <^lder lives lefs ; but never incon-
fiderable, except in th^ oldeji lives.

It appears, .therefore, that, ip confequence
of fucn a vi^ay of raiiitJg money, the public
muft always pay much more in intereft than
th^rc is any occafioq for y j^nd wajie a fum
nearly equal tohalf the principal borrowed {a).
This, however, tho' lb Avafteful, is a more

frugal

■ «

[a) It is' obvious, that the obfcrvatrons here made^
may be applied to the commoo methods of rjifing money
en life-annuities, for building churches, paving ftfeet^,
•making navigations, &c. &c. And, in general, to all cafes
where the money rectivcd, is not laid up to be improved.
•^For, to view this fubjecl in- another light, kt us ftip*
pofe 1 0,900 /« borrowed for any public work, on perpe-
tuities, at /^per cent. And, if that will a^fFord xfiove tnr
,couragement, let them be made irredeemable for any
number of years lefs than fei/eiueen. Let us further fop*
pofe, fuch rates,, or tolls, eftabliibed for the payment of
the intereft aqd principal, as fliail produce double the ior
tereft of th^ fum borrowed 5 or 800/. per annum^ inflead
of 4ro /. per annum. Let thejierplus^ a's it comes in haip-
jfearfyy bei laid up to accumulate in the public fiuiiis. ' ^ia
47 years and a half, reckoning intereft at 4 per ^ent. a ca-t
pital will be raifed, equal to' the whole fum borrowed i
and, therefore, at the end of that time, the whole debt
ioay be difchargcd, and the whole tranfaclion finiibed>.-^
But if the fame fum had been borrowed on annuiiied, ior

ih^

and the National Debt. • 153

frugal way of procuring money than hy bor^
rowing on perpetuities^ without putting them
into a courfc of rcdcniption j for in this cafe,
(if a fpunge is not applied) the lofs mud be
infinite.

I muft add, that thcfe obfcrvations are par-
ticularly applicable to all the ways of railing
money by the fale of reverfions. — The pub-r
lie, for inftance, might procure a million, by
cfFering for if a fupd, that will be difengag-
cd at the end of 1 8 years j and then produce
80,000/. /^r annum for ever. This, fuppo-r
iing intereft at ^per cent.y wQuld be the very
fame . with offering two millions, 1 8 years
hence, for ane million now : And 9 private^
pi an, or an office for the fale of reverilons,
might gain by fuch a tranfadtion ; becaufe^
the money advanced, in confequence of being
improved, might, ip 18 years, be more than

tl^e liyes of a fet .of perfqns 50 years of age, at 8 ftr ant.
which is I /. pit ctHi. left than the trae value of fuch an-
nuities ; Had this, I fay, been done, half the annui*
{ants would h^ve been alive at the end of the term I have
mentioned ; (fee Tables III, ly, and V,) and the whole
tranfadicn, together with the expences and trouble at-
tending the management of it. could not have been finally
clofed 'till the extindion of all the lives ; that is, not in
lefs time, moft probably, than 35, or, perhaps, 40 years.
«r— It is a neceflary ob&rvation here, diat, if public credit
maintains its ground, much will not depend, in the plan
now prbpofed, on the rife and fall of Stocks. If a war
fuiks them, the money laid out, while the war lafts, will
accumulate fafter. If a peace raifes them, the money
lh«t had been pfcvioufly laid out will be proportionably
JQcreafed^

doubled,

J 54 ■ Of Pubtic Cridtty

doubled. But, as the public always borrows
for immediate fervices, and never lays up
inoney, it would neceffarily lofc a fum equal
to the whole fum ' borrowed : And the fame
money might have been borrowed on a fund,
producing 50,000/. per annum ; which woul4
not only pay the intcreft, but difchargc the
whole principal in 41 years (j).

By raifing money on life-annuities, the
prafent membef's of a ftate take a heavier load
on thcmfelves, in order to exempt pojlerity \
and there would be a laudable generofity in
Ihis, were it not fdf ihcfoliy of it ; thp fame
exemption being ecjually prafticable at half
the expence, — On tne other hand. By bor*
towing oh reverfioriary grants, the prefcnt
membefs of a ftate exempt themfelves entire^
hy by throwing chc load doubled on pofterity j
dnd there is a cruelty and injuftice in this
that nothing can excqfe.

It is well known, that both thefe methoda
of railing tnooey hftve been pradtifed among
us. This, however, is„ by no means, the
worft that has been done. It has been (:ommoA
to borrow mooey to pay the interefi of md-*
ney borrowed, and thus to give compound in--
tereji for mopey y a^d our parBamenU bavcj^

(a) The finalteefs of tkd iiiins, wfcick I hare here and
^Ifewhevd fofneti]ne& fupfiofed (o b« employed in dif-
charging the pubUc debts, can create Dd difficulties, 'be-
^aofe tMre is no ftun wbkb may Mt be applied lo tbU
ufe by purcbafing ftock.

-- • foment

wd th$ NatUnal Jbeht. k 1 5

jgDinetiineS;, expefsly provided^ that this fhall
^e done for a fucpeiiion of ycar^^
But to return.

The epquii^ which hal occafioned thi|
^igrefiion^ muft be highly interefting to e^ery
pcrfon who wiihes well to his country.— All
fchemes for diichargipg the publip debts, by
life^anpuiticfi, have been Ihewn to be abfiir4
and extravagant.— In general 1 it fnay be ob-
fervedy that it is far from probablei that any
pK>ney which the nation can fpare, if ap^f
plied fo as to bear only Jimpff jntereft, can
De capable of reducing its debts within due
bounds ; or of doing us, in oqr prefent cir^
pumftanceS| any efiential fervicc. A fuild»
producing a furplus of even two milliofi; anr
fiually, would, when thus applied, pay nQ
more than 40 millions in 20 years 1 and, in
that time^ a war plight probably come^ which
would interrupt the application of it 5 and
increafe our debts mucl^ znore than fuch 2^
|und had leifened them.

Certain it is, therefore, that if our aft^ir^
are to be retrieved, it muft be by a fund in^
creaiing itfelf in the manner I have explain**
ed- The fmalleft fund of this kind is, in^
deed, omnipotent, if it is allowed time to ope-
rate.' JBut we are, I fear, got fo near to the
limits pf the refources of the nation, that it

canno( be allowed much time : And> in orr

* • ^_

der to make amends for this, it is necefiary

'■■' ' ■■ '■ '■•'■ ' ■ that

tS^ Of Public Credits .

that it fliould be large. — Let us then fuppofe,
that the nation is ftill flrong enough to ena-^
ble it to provide a fund, that fhkll yield a
million and half annually ^ for 20 years to come :
And alfo, that, together with all its prefent
burdens, it is capable of bearing every addi--
tianal burden that 20 years more dan bring
upon it. If this is not true, we have^ I think,
nothing to do but to wait the iffue, and
tremble*

A fund, producing annually a tnillign and
a half, \vould increafc to three millions ^^r
ann. in 20 years {a). At the end of this term,
the, nation might be eafed of the moil op*
pre0iv6 ta^e&j to the.amount of a million and
^ half i and the confcquence would prove,
that, if there ihould have been a war, either
th? whole, or much the greatcft part of the
addition occafioned by it to the public bur*
dens, would, be tak^n off, and the nation
reinftated nearly in its prefent circumflance^*
But, if ihgre. fliould have been no war, the
national debt, and th^ taxes charged with it,
would be reduced a third below xhe fums at
which they now ftand ; and the nation would
be fo much relieved as to be prepared for a
war.-r-Tb^ remaining million and half would,

"(a) It fliouId be remembered* ibat in the year 1781,
1 L per cent, on the confolidated 4 per cents, will be finni-
hilated, ^n^ that I fuppcfe the favings derived from hence
to be t^en at that time as a part ot the fund. — Methods^
might be eafily contrived for getting this faving ioune-
^ifiiely, wbrch wouid he fome advantage.

in

and the Nathml Debt. i 57

In 23 years, iocreafe again to three millions
per annum \ and then, fo.mach more cf the
public taxes woold !bc fet free y 50 miliions
more, or 9*^^11111008 in allv of the public
debts would be difcfaargcd, and the dij£cul-%
ties of the nation would be, • in- a great mea*
fure^ CQnquered.~«Duidng this whctkcourii)
of tlme^ there majr .pof&blyt be but one war;
and (hould that happen, the appropHatlon at
the end of It, of about 400,000 L per annum^
might be enough to anfwer all purposes.

In thefe obfervatioos; I; fuppofe the 3 per
cent 5^ to be paid; off 2Xpar,\ and no advantage
taken at any time :o£ their i law price. By
taking this advantage^ and ;with the help. of
a little management, a fund, producing an*
nualiy a million and half, • might be made to
increafe ffo .another million and half, in kfs
time than I have ailigned. Should thece be
a war in a few years, the 3 per cents, woiild
probably fall below jK^y and then the pro<^
prietors of them muft be glad to pact with
them at this price ; the confequence of whicb»
fuppoling. the war to laft eight years, wodi4
4>e, .that the fund would (kmble itfelf, and
the nation be relieved in the manner I have
mentioned, in 18, inftead of 20 yeafs.^-^
The advantage will be the fame, fiippofing
the government at fuch a time to go on in
paying off the 3 per cents ztpar. i?or the effect
of this would be, that money might be bor-
rowed for the public fcrvicc on proportion-
I ably

t^S 6fPuilicCreSh

tbly b^ter terms. Suppoie^ for. inuftnc^i
that foor millions . muft be borroMred fbr the
ftrvice of the yriai: $ . and let the prodmce of
the fond be the^i incxeafed^ to two irttllions %
ftiid the mtemft of moncxyin they&cfcr^ ah&vir
4 ;^^ ^M/* la thefe ^ircumftanoes> it would
be the .ioteieft of the lenders of moneys td
take j4 ^^iT iii»;i/» for the /inns they a4traiiced|
in confiderafeion of having their 3 per tentu
paid G^ at far^ to the amount, of half thefe
fums.'^^War^ therefore^ would acoekrate the
redemption of the public debts \ '. and it would
do this, the more, the longer i^ laftod, and
the higher it raiied the intercAof nymey^
Or iff in corffequence of paying ii ways at
fdr^ thia could not happen i an equivalent
efieiQ: would be produced in the. way juft
ilidntioQid. The flocks would be always
kept up by die operations of the fund 1 and^
in proportion to the fuqis yielded by it, the
pofadic orookl be abb to borrow mbney more
ddmntagjeotiily, and lefs would be added td
its burdensv^^Thls ieems .to me an obferva«*
tiMv o£ particular ctmfequonee^ It demons-
Arates, dkati tln& mo variable application^, ih
■^ar is well as fencey of die prdduce of the
ittnd I am fiop^ofing^ io the payment of
the qaiional dtbts^ rather than to aosy cur^
rent fervices, would, independently of its ef^^-
toGt in {a) redoen^ing thefe debts,, be attends

ed

(a) So tnie 19 ihJ9i th^^a wai*, wer« tfc now engaged
in it, wouM only render the pTy/int tiaie fo much the

more

4nJ the i^fatitnai t>eiti . t ^9

«d VI th great advantages to the puUic. But
this is.a lubjc^ oa which I (hall have occa^
fioD to fay ^ore presently. The

more proper for entering jnto m^afvre^ for pajtQg th^
public debts. And the following obfervattpns will put
this out of doubt.

. As it ^ now bcootKi tM prtftico to fasie lemoife t^
ktHri^i in p€^9 wc qu)^ fae furc^ that ix^ joir will p9^
without them in Wftr,, ' I woufJ, therefore^ propofe, that^
infiead of making life of them in raifing the annual fup-
pKeirin war, they ilioiiU be then applied as an aid in diT-
ct)4u:giiig tlie public ,dfb^-v^&Uppoiie the war to laft i<^
y^ars, and the ^fer c/n^s. at jcx — Suppofe alfo, each lot*
Ifty to confift of 7*^0^000/. in tidftSy which, when dif^
pofed of to &ibf<(ribtr^, Wilt bfing in 1,050,000 /r Oa
ibef^-ftippoTulonSyihd whU^/^ tp the piibiif, froni ap«
plying the lotteries to thf payiijept of thp pul^lic debt^,
rather than to the current fuppjies, will be 1,050,000 A
amrntlly) or to mfltlofis anfl i in alk — The gain wiH be
^ ^loiM : 7 5Q,oo<) /j ^: t|)^ prodnpo of th« fipking f und^
formed into ticicets, will, b^ tb^ iame with i,P|0^oo/. }
and this fum will pay o^ a miljion and a half of the ^p4r
ittmy Of ery year^ oi^ ^5 mflljong in all ; and the gK>win^
favings arifing from thefe payments, will, at the end ^
10 years, have paid, at leaft, two millions more. The
nation, therefore, having paid ofFa7 millions of its debts,
arid added to them only lO millioxls and ^9 will gain fi^
tlriUr9n» and 4. . But 2ilii» will be the fmalied part of ica
gaiHf* All the produce oftk^Jmihigftmit ever and abomi
750,900 A might be charged with the payinent of the in-
tereff of iiich new debts as would be neceflary to be con-
MaAed during the war ^ and, at the end of it,. the nation^
with the help of 200,000/. to be difengaged in 1781, by
tH^ r^duftif n of the ^^ertmts^ would fiml itfeif poffibfled
4^f a^SuuCppoducinji ?)4vS0»^^^ A annuallj^ ^ which, faith-
tMlly empfojred, imght jpcobably be fufEcient to extricam
It from all its difiiculties.— ^Beiides this \ fuch a fchemo
would not QiHy^ffirve^ hut nfifi and tA^ifi^ the credit
of the public ; And he only can be duly fenfibje of the
iinportancc of this, who will conilder, what danger there

would

t6b • OfPttilictlrrM '

lihQ Jinking fund^ in its prcfcnt ftate, Artrf/
after- fupplying- the deficiincics of the ptac6
eftablifhment, yields, Ifappofc; a confidera-^
ble part of the million ^nd a half I have men-^
tibned. An aTmua! lottery might eafily raife
206,606 1, nibre. fiut this is a meafure which
I cannot wi^ to fee" carried into execution^
unlefs abfolntel? ncceflary. Were the ma-
hagerSv.of our anl^rs fufficiently in earnefl in
this bufinefs, t cannot doubt but that fuch
fevings^ might be made in the colleftion'and
€3fperidtture of the national revenue, as would
caufo" the finking fttodl^to yield, for 1 8 ot* 20
years to come, the W)&*/r of this fum; \^rrth'^
otit im poling any new burdens on the pub-f
lie. But, vcTQ there, indeed, no way r.of
providing any part of k, but by creating nev?
funds, or impofing n^w taxesr'^ it QUgA't to be
done> . becaufe.it mufi be dope, or tne nation

fink. ? * : . .

. < ■

The evils and dangers, attending an ex^r^
bitant public flebt in this country, atre fo greats
that they cannot be exaggerated.— Withont
repeating, \vh at has been io often faid, of its
increafing tjite dependanco on^ the crowny

would he in another war, ifaotrid it continoe iMg, of ei-^
ther dvertuhehmng puMit Credit.; or of bdog terrified, b^
the apprehenftoR of fuch a calamity, into an ignominious
and faral peace.* The cftablifhmcnt, therefore, offomif
fuch {)hn as that now propofed, wodld, at the beginning
of a war, be the moil iitiportant of all w'oc^cs.

render'

\

and the Nat tonal Dibit. 1 6 f

iroinderiog' us tributary to fbreignisrs; and
railing the price of proviiions and labour ^
aad» confequently^ checking population; and
loading our trade and manufadures ; I will
only take notice of the following evils which
attend it.

Firft; The execrable J)radice8 of the
alley. Thefe cannot be Mentioned in lan^
guage too ftrong. They arc growing every
day ; and the national debt^ by giving occa--,
fion to them» is likely foon (with the aid of
annudl lotteries) to ruin all honeft induftry.
among U8» and to turn us into a nation of
gamblers;

Secondly. It ihuft check the exertion^
of the fpirit of liberty in the kingdoni. The
tendency of every government is to deipo-
tifm; and in this it muft end, if the people
are not conflantly jealous and watchful. Op-
pofition, therefore^ and refiilance^ are ofteil
heceffary. But they may throw things into
confufioUi and occafion the ruin of the public
funds* The appreheiifion of this mitfl; in^
fluence all who have their intereft conDed:cd
with the prefervation oi the funds; and in^
dine them always to acquiefcence and fer^
Vility.

But further. It expdfes us to particular
danger from foreign as well as domejiic ene-^
mies^ by making us fearful of war; and iri^
fcap^ble of engaging in it, however necefiary;

M With-

i6l OfPidlicCreSt; .

i^tthoat the hazard of bringing on tenibfo
convulfionsi by overwhelming public credit.

All thefe are evils which muft increaib
Ifrith tvtty increafe of the national debt j and
there is a point at virhicb^ whci) the^ arrive^
the confequences mufl be fatal (tf)«*^I am
now writing under a eonvidton, that I am
doing the little in my power to preferve my
country from this danger. I have dacwng that
an annual fopply of a million and a haljf for 1 8^
Of at moift 20 years, might probably be made
the means of reftoring and favtng tts« This,
therefore^ is our remedy i and it ought to
be applied immediately^ lead it ihould not b^
applied time enough.

But to proceed to fome further ck&xv^
ttons.

What has been faid, Jbas all along fiip^
poied zfacredznA twoiolaUe apiplicatioQ of th«
fund I have defcribed, and of all its earning0«
to the purpose of finking the national debt*
The whole effi^ of it depends on its being
allowed xo corals, without itfT£&E.u:^-^
Tio V9 a pnoper time. But it may be afl&ed^
how this can be fecured ? Or, by what roc^
thod an objed, that, muil be ooiitinually
growing more and more tempting, can b»

, (al ^ Eith^ fbe natioa (Mr. Hmjm fajs, %S^yp
Vol. JJ. p. 145,) muft Jeftroy public Credit ^ or publk:
^ credit will deftroy the nation.'*

delcnd«d againft invafion and rapine ?^^I
inight here mention the fu peri n tendency and
care of the repreferitatives of the kingdom^
the faithful guardians of the ftate, to whom
ininifters al% refponfii3ile for the ufe they
malte of the public Money. But e^rperiencK
has Ihewn^ that we cannot reiy on this fe^
«arityi-i^The difficulty, therefore^ now men*
tioned> is the very greateft difficulty the na«
tion has to ftruggle With in the payment of
its. debts;

The finkiDg fund wa« ei|ablif))4id in thtf
year 1716, or fotin after the acceflion of th*
pt-efcnt family^ at a time when the public
debtSi thd' not much more than a third of
What they are now^ were thought to be io
con(iderable as td be alarming and danger-
ous. It wai intended aft a SACRf:D depo^
«IT never to be touched j the law which
^ablilhed it declaring^ that it was to be ap«
plied to the payment of the principal and in«
teped of fuch national debts ^nd incuQibran^
tesi as had been i/icurred before the 45th of'
Detemier 1716 i and t^ M otbir ufii inUnt ^f
purpofi wSat^ver i'-^Tht faith of p^irliamfnti
therefore^ as well as the fecurity of the kiog^
dom^ feemed to requinei chat it ifilould b«
preferved carefully and rigoroufly f^otn alie*^
nation; Bat^ notwithftandi^ig tbis^ it has
been generalfy alienated ; and the prpduce of
it employ^di in helping to defray fuch ciir^*

M t rcQt

i64 Of Public Credit\

rent expeoccs as the exigences of the ilate
rendered neceflary.

In order to juilify this, it has been ufual
to plead, that when money is wanted, it
makes no difference, whether it is taken from
hence, or procured by making a new loan.
There cannot be a worfe fophifm than
this. The difference between thefe two
methods of procuring money is no lefs than
infinite. — For, let us fuppofe, a million want-
ed for any public fervice. If it is borrowed at
4 *^r cent, the public will lofe by the payment
of intereft 40,000 A the firft year, and the
fame the fecond year, and the fame for ever
afterwards* But if it is taken out of the
Jinking fund^ the public will lofe 40,000/. the
iirft year j 40, 160 /. the fecond year i 8o,ooo/.
the 1 8th year; a million the 85th year : For
thefe are the fums that would, at thefe times,
have otherwife neceffarily reverted to the
public. It lofes, therefore, the advantage of
paying in 85 years, with meney of which
otherwife no ufe could have been made, twen^
tyi^Jive millions of debt.— In other words ; by
employing the sinking fund, in bearing
current expences, rather than borrowing new
money on ne^ funds ; the ftate, in order to
avoid gvnti^sfimple interefi for money, is made
to alienate money, \that mufi have otherwife
heen improved at compound inter ejl ; and that,
in time, would have neceJjarUy increafed to any

. . . fum*

and the National Debt. \ 6 5

fum. — Had a faithful ufe been made from the
firfl',of onlyone third of the produce of this
fund, the greateft part of our prefent debts
would now have been difcharged (<^).—
Can it be poflible then to think, without re--
gret and indignation, of that mifapplication
of this fund, which, with the confent of
parliaments always complying, our minifters
have pradifed? — It is difficult here to fpeak
with calmnefs. — But I ioth^zr.^'^Calculation^
and not cenfure, is my bufinefs in this work,

(a) Sec the ^eflions at the end of the Appendix.

The principal obfervitions in this Chapter, I have
given juft as they occurred to my thoughts, without know?
ing that any of them had been made by other writers*
Sonne propofals and obfervations of a fimilar nature, I
have fince found in an excellent pamphlet publiflied in
1726, entitled, An EJfay on the National Debts of this king*
domy wherein the importance of difcharging them is confidered^
andfome general mijlakes about the nature and efficacy of the
Sinking Fund examined and removed. In a Letter to a
Member of the Houfe of Commons. Fourth edition.

I muft beg leave to add, that in a pamphlet publifhed
fmce the former editions of this Treatife, and entitled,
An Appeal to the Public on the Subjedf of the National Debt^
I have endeavoured to explain iuch parts of this chapter
as have been thought not fufficiently clear ; and given a
more full account of the nature^ powers and hijlory of the
Sinking Fundy and of the pernicious confequences of thofc
alienations of it which I have cenfured above, and which
for many years, have made a part of the fixed practice of
government among us.

M 1 ESSAY

[ »67 ]

ESSAY I.*

Containing Obfervations 9n the Ex-r
pcftations of Lives ; the Increafe of
Mankind \ the Number of Inhabit
tunts in London ; and the Influx
ence of great Towns y on Health and
Population,

In a Letter to Benjamin Franklin^
^fp L.L.D, and F.R.S,

Dear Si r^

I Beg leave to fubmit to your perufal th^
following obfervations. If you think them
of any importance^ I (hall be obliged to you
for coqimuaicating them to the Royal So^.
ciety, You will nnd, that the chief fubjed^
of them is the prefent ftate of the city of
liOndon^ with re/pedt to healthfulnefs an4
number of inhabitantSi as far as it ^r^n be
CoUeded from the bills of mortalityt Thij
is a fubiedt that has been confidered by
others i bvit the proper method of calcqlating

* This EiTay was read to the Royal Socikty,
April 27tb, 1769, and has been publiihed in the Philo-
ifophical TranfaSions, Vol. 59. It is here republKhed
with corre£Uons ^ and feveral additions, particularly th«

M 4 frorn

J 68 On the ExpeBation of Lives i

from the bills has not^ 1 think, been fufH«
cicntly explained.

No competent judgment can be formed of
the following obfcrvations, without a cleat
nption of what the writers* o?i.Lj/^-^«««z/*w
and Reverfions have called the ExpeBation of
'Life. J^erhaps this is not in common pro-?
pcrly underftood i and Mr. D^ M«wf-s man-
ner of exprefline himfelf about it is very lia*
blc to bemiftaKen.

The moft obvious fcnfe of the expeBation
pf a given life is, ^* That particular number
f i of y^ars which a life pf a given age has aig^
f^ equal chance of enjoying/' This is pro-
perly the time that a perfon may reafonably
expeB to live ; for the chances againji^ his Kv-
ing longer are greater than thofeyir it; and,
therefore, he cannot entertain an expeSlation
6f living longer, confifteptly with prouability.
This period does not coincide with what the
ivriters on Annuities call the expeSlation oflife^
except on the fuppofition of an uniform de-
f reafe in the probabilities of life, as' Mr.
Simpfon hz^ oblerved in his SeleB Exercifes^
p. 273. — It is neccflary to add, that, even on
this fuppofition, it does not coincide with
what is called the expeSiation of life, in any
pafe of joint lives. Thus, two lives of 40
have an even chance, according to Mc. De
Moivre's hypothefis (tf), of continuing to-
gether only 13T years. But the expeBqtiptt^

{a) See the Notes in page 2 and 23. . % .

•^■'■/ ' 'of

the State ^/Xondon, Population^ &c. 1 69

fif two equal joint lives» being (according to
the fame hypothelis) always a third of tl»
common complement i it is, in this cafe, 1 54year8«
It is necefiary, therefore, to obferve, that
there is another ienie.of this phrafe, which
ought to be carefully diflinguidied from that
BOW mentioned. It may fignify, ** The
^^ mean continuance of any %x^^nfingle^JQinU
** oxfurviving lives, according to any givem
^^ Table of Obfervations i* that is, the num^
her of years which, taking them one with
another, they adlually enjoy, and may be
confidered as fure of enjoying ; thofe who live
or furvive beyond that period, enjoying as
much more time in proportion to their num-
ber, as thoie who fall Jhort of it enjoy lejs*
Thi^; Suppofing 46 perfons alive, all 40
years of age ; and that, according to Mr. De
Moivres iypotbefis^ one will die every year
'till they are all dead in 46 years ; half 46, or
2 3> wiU be their expeSlation of life : That is 1
The number of years enjoyed by them all,
will be juft the fame as if every one of them
had lived 23 years, and then died; fo that,
|appo£ing no tntereft of money, there. would
be no difference in value between annuities
payable for life to eveiy iingle perfon in fuch
a &t, and equal annuities payable to another
equal fet of perfons of the fame common age,
fuppofed to be all fure of living jufl: 23 years
^oid no more«

la

ij^e On iSe Explication ff Lives }

In like manner ; the t&ird of 46 years^ or
15 years and 4 months (a), is the exfie&ati^n
of two joint lives both 40 ; an4 this is alfb
the expiration of the farvivor« That is;
iuppQfiiffg a fet of marriages bttwfen pericus
kll 409 they will, one with another, laii juft
tilie titne 1 and the forvivors will laft tbe firing
^tine. And annuities payable during thoicon<r
f iimance of fach marriages would, fujf\poiing
tio inreref^ of money, be of exactly the ianlt
^al<ie withannuities to begi^a at tbe extino-
tion of fuch marriages, and to be paid, during
4i&, to tbe furvivors.-^^^Iii adding together
Hhe years wbicii any great* number of fucii
tiiarrtnge^afnd their furvi\tM-^ips, bavc lafted||
the Autis would be found to be eqaal, ,

One is naturally led to underftand the
tKpeSUtvM of life ixi the firft of the* ftufes
now explaijied, when^ by Mn Simffan and
Mr. De MQivre-^ it is caUed, the number of
years whivh^ upon an e^akty^f chance^ aper^
Jon may e^eSi to en^y % or, the time ^wbich a
ferjon (fa given age fntyjt^ expe& tc contmwe
in being \ and, in the laA ienfe,^. when it is
icalied, the Jbare f life due n a perfon. But^
^ in reality it is always ufed in the. laft
of thefe fenibs, the fbrmer language^ibould
not be applied to it ; And it is in this laft
ienfe^ that it coincides with the fums of the
frefent probabilities, that any given fingic
or joint lives (hall attain to the en4 of the

{a) Sec Note (L) Appendix.

jft.

the State of London, PopuUthi^f Ice. 171

i9i^ ady 3d, &c. momenUf from this time fak
the end of their pofiSble exiftence i iH^ (in
the caie of furvivor(hips) with the iVim of the
probabilities^ that there iliaU be a furvivor at
the end of the i ft, 2d, 3d, &c. momentai
(foo^ the prefent time to the end of th^
poflible exigence of furvivorfliip. This coin^
fidence every one converfant in thefe fubjedi
li^uft fee, Qpon refledinff, that both tbelb
fbafes give the true preient value of a life%
annuity, fecured by land, wkhOut intereft of
money {a).

. This period in joint live^, I have obfetv-**
^ is never the fame with d)6 period- which
they have an equal chance of enjoyif^ ; mad
in fingle lives, I have obferved, they are Um
fame only on the fuppdiitiori of an uniform
<lecreafe in the probabilities of life. If tbik
^ecreafe, inftead of being always uniform, if
ficcekrated in the laft ftages of life 1 the for^
iner period, in iingle lives, will be /e/i thaa
the latter 5 if retarded f it will be greater.

It is neceflary to add, tltat the number
ipcprefiing the forn>er period, multiplied by
^ number of fingle or joint lives whoie ex*
pedlation it is, added annually to a fociety or
;own, gives the whole number living toge«-
ther, to which fuch an arniual additioo
woiUd in time grow. Thus; fince 19, or
fbe third of ^j^ i« the expeSsthn of two

[a) See Npte (L) in the AppcQd^i

joint

iyt On the ExpeSfation of Lives i

joint lives whofc comtiion age is 29, or com-*
mon complement 57 ; twenty marriages every
year between perfons of this age would, in
J7 years, grow to 20 time& 19, or 380 mar-
riages always cxifting together.- The nuih-
hit oi fUrvhors 2i)io znimg irorn thefe mar-
riages, and always living together, would, in
tlvicc ^y yciirs, increafc to the fame number;
An<3^ ' fincc the' exptSiation of a finglc life is
always hsXiXt^ -complement y in 57 years like-
ivife, 20 iingle peffons aged 29, added annu-
ally to a town, would increafe to ao tihies
^815 or 570; and, when arrived at this
fiifi^ber, the deaths every year will joift equal
Ibe acceflions, and no fxirther increafa b^
fiofllble, : ,

; :Ic appears frcfm hence, that the* parttcu-*
iar proportion that becomes extindl every
year, out of the whole number con ftantly
exifting together of Iingle or 'joint livcSj
inuft, wherever this number undergoes no
variation, be exactly the fame with the ex-^
feBatitm of th6ie lives; at Jhe- time when
their exigence commenced. Thus; was it
found that a 19th part of all the marriages
among any body' o^f men, who(e numbers do
«ot vary, are diflblvcd every year by the
deaths ^of either the huiband or wife, it
would appear that 1 9 was, at the time they
were contra<fled^ the ec^peSlativn of thefe
marriages. In like manner j was it found
^jn a fociety, limited to a' ^xed number of
- memberSji

the State ^London, Population^ &c. 1 73

ittenbersy that a 28th part dies annually out
of the whole number of members^ it would
appear that 28 was their common expe<fta<-
tion of life at the time they entered. So
likewife ; were it found in any town or di-*
ilridt, where the number of births and burials
are equal, that a 20th or 30th part of the
inhabitants die annually, it would appear,
that 20 or 30 was the expeSiation of a child
juft born in that town or diftridt. Thefe ex^
peBations^ therefore, for all lingle lives, are
eafily found by a Table ofObfervations^ (hew-
ing the number that die annually at all ages,
out of a given number alive at thofe ages ; and
the general rule for this purpofe, is " to di-
^< vide the fnm of all the living in the Table,
*^ at the age whofe expedhttion is required,
and at all greater ages, by the fum of all
that die annually at that age, and above it ;
or, which is the fame, by the number (in
the Table) of the living at that age ; and
half unity fubtraded from the quotient will
be the required expeSiation {a).'* Thus, in
Dr. Halley's Table, the fum of all the living
at 20 and upwards is, 20,724. The number
living at that age is 598 ; and the former

(a) This rule, and alfo rules for findine in all cafes
the expedations of joint lives and furvivorihips, may b«
deduced with great eafe, by having recourfe to the doc*
trine of fluxions. In this method, Mr. De Mmvn £iys,
he difcovered them. See Appendix, note (L), where an
account will be given of thefe dcdudlions, omitted by

Mr. De Moivre.

• ...

number

€€

ffC
€€

1 74 ^ ^^ Expe&aikn cf JLh^s $

fiumb^ <Myiidc4 hy the hM^u and half littitjr

{a) Aib|ra(^e4 iVoia) tbe iqiimii&Qt^ gives 34. 1 5
for i)M i»^€J^m «f aoi Tbe rxpeftatioil
ef the £irme Uf^p by Mn Bivtpfotis Tabki
formed ^pm {he bills of moruiity of hm^

• «

(tf) If wc conceive the ttctuh neceflary to fupj)!/ the
tc^iTof^vefy year to be made always at the ihi^ th^
fWr tto tvidend ougbc so be tte muium between <M
oytnbers Itrixi^' ax the Uginniftg ^d tb^ iiii 9f th(B yea^;
That 13, it ought to b^ <al^en J^s it^ap xhe fuip of the liv-
fngtn the Table at aod above the given age, by ^^tbe
imtofaer diat jdie in Xke year j the «lle£t of which Jmitm^
I/m vtiU be the fa^e with x\itjkitrin&i«n beve direQ^d.--'
The rea(qn of this fiibtr^^iofi wUi he furtber explaiaed^
in the beginning of the laft Efjl^y.

{i) Ic appears in«p« 169 and iryo, that the txpe^atims oJF
^/iff/tf i^ikd /j/V live^ fee icM finiie whh ithe values of tfvnrf^
i«fj on thelp Jiv.es, fuppofing jio ixueceft or improv^oieiit
of ntoney.-^In confkiering this fubjeflj it will, probably^
Mciur to fome, thac, i^Uowtng intei;e(tfor money, the valued
pf Jiya tmA . br ^e An^e with itbe ^abiiefi of anouities
Urtainfoi » ^lumber of veara eicjufil to the ij^fflaihns g(
the lives. 'But c^re tnuvt be taken ;iot to fall into thi$
miftake. The latter values are always greater than the
forqarr: And thieTpaibais^ ithft, Iha^ a number of/bigk
qr joint liy,ea QfgW^fi ages wit\$ am^g th^oi, cjfjOf ^ ^/*
twjiumber of years^ yet foine of tbeni will )?njoy ajQuch
gteatiTj and fome a much icfs pumber of years. Thus ^
100 makriages among perfqns, ail ^9, would, as I have
faid, one with another^ exift 19 years 3 and W .o^cc!
bound to p^ annuities to fuch marriages daring their
eontimiaiice, ^inigbt reckon upon ihakin^ 19 payment^
for each Hiarrlage. But then, many of v^tk jpaymenis
jrouid ti«t be 4nade 'tUl the end of 30, and fome not *tiU
the .and of 40 years. And it is apparent, that on account
^f ttfae gGcat(pr value of ^uick than late payipents, when
money £«r; intereft, 19 payments fo made cannot be

wortk

• the StaU of Lov^iiM, Population, Uc. x^pJ^

- Tbeft obfervatioos bring me to the prin*
CJpal point which \ have bad all along ia
vi^w. They fiiggeft to lu an eafy method
of finding the number of inhabitants in a
place, from a ^aUe tf Obfervatkns, or the
kiU$ cf mortality for that place, fuppoOng the
y^early births axid burials equal. '^ Find by
** the Table, in the way jufl: defcribed, the
^^ eKpeSlation of an infant jufl: born^ and thisj^
f^ multiplied by the number of yearly births*
'^ will be xhz number of inhabitants." Ac
BreJlaWf according to Dr. Halley*% Table,
though half die und^r 1 6, and therefore aa

worth as much, as tbf faine number q( payin€iit« mad^

regularly at the end of every yeai) 'titl in 19 years tjiey
are all made.

This obfervation might be empIoyeJ^ to demdnflritc
Airtber, the txttt of thofe wko have maidtainedg that tbp
value of a given life is the fame, with the value of an an«
nuity certain, for as many years as the life has an equal
chance of exifting. Were this true, an annuity on a life,
fuppofed to be expofed to fuch danger in a partsctdar year,
^ to create an equal cb^pce, whether it will not fail that
year, would, at the beginning of the year, be worth nv^
things though fuppofed to be fure of continuing for ever#
if tt efcaped that danger : nor, in general, would th«
values of annuities on a fet of lives, b^ ftt all ^ffeded by
anv alterations in the rate of mof tality among them, pro-^
Tided thef? alterations were fueh, as did not aifet^ the pe^^
s^od dunng which they had an equal chance of -eKlfting^
^«>— But there can be no occafion for taking Rotipe of an
ojfinion, which has been embraced only by pcrfohs ig«
nprant of mathematics, and plainly unacquainted with
the genuine prmciples of calculation on this fubjeift.—>(
See a pamphlet on Life- Annuities by fVepmm Lee^ ££93
of the Inmr TemfUi '

7 Infant

176 On the ExpeSDation of Lives i

itafant jud born has ^h equal chance of liv^
ing only 1 6 years ; yet his expeSation^ found
by the rule I have given, is near sS years 1
ftnd this, multiplied by 1238, the number
born annually, gives 34,664, the number of
inhabitants. In like manner, it appears front!
Mr. Simpfon's Table, that> though an infant
juft born in London has not an equal cbanci
of living 3 years, his expeSiation is 20 years j
and this number, multiplied by the yearly
births, would give the number of inhabitants
in London f were the births and burials equal ;-^^
The medium of the yearly births, for ted
years, from 1759 to 1768, was 15,710. This
number multiplied by 20, is 3 14,200 ; which
Is the number of inhabitants that there would
be in London^ according to the bills, were
the yearly burials no more than equal to the
births : that is, were it to fupport itfdf in its
number of inhabitants, without any fiipply
from the country* But for the period I have
mentioned, the burials were, at an average^
22,956, and exceeded the chrifleaings 7,246*
This is, therefore^ at prefent, the yearly ad*^
dition of people to London from other parts
of the kingdom, by whom it is kept up^
Suppofe them to be all, one with another^
perfons who have, when they remove to Lon^
don^ an expeSiation of life equal to 30 yeaw.
That is I fuppofe them to be all of the age
pf 18 or 20, a fuppoiition certainly far be-^
yond the truth. From hence will arifc, ac-
♦7 cording

the State g/*London, Population^ &c. 177

cording to what has been before obferved^ an
ftddition of 30^ multiplied by 7.246 ; that is#
217,380 inhabitants. This number^ added
to the former^ makes 531^5^0; and this» I
think, at moft^ would be the number of in-^
habitants in London were the bills perfedt.
But it is certain, that they give the number
of births and burials too little. There are
many burying places that are never brought
into the bills. Many alfo emigrate to the
navy and army and country } and thcf^ ought
to be added to the number of deaths. What
the deficiencies aridng from hence are, can-
not be determined. Suppofe them equiva-
leiit to 6000 every year in the births, and
6ood in the burials. This would make an
addition of 20 times 6ooo> or 120,000, to the
laft Dumber i and the whole number of in*
habitants would be 651,580. If the burials
tre deficient only two-thirds of this number,
or 4000 ; and the births the whole of it ;
20 multiplied by 6000, muft be added to
314,290, on account of the defeds in th^
births : And, tinc^ the excefs of the burials
above the births will then be only 5*246 1
yo multiplied by 5,246 of 1579380, will be
the number to be added on thi^ account 1
and the itim, or num^ber of iAhabitancs, wiU
be 591,580.*— But if, on the contrary, the bu-
tials are d^^cient 6000, and the births only
4900; 80,000 muft be added to 314,290,
on account of the deficiencies in the births ^

N and

178 On the ExpeSlation of Lives;

and 30 multiplied by 9,246, or 277,380, on
account of the excefs of the buriak above the
births ; and the whole number of inhabicantf
will be 671,580.

Every fuppofition in thefe calculations
is too high. Emigrants from London are, in
particular, allowed the fame expeSlation of
continuance in London with thofe who are
born in it, or who come to it in the firmeft
part of life, and never afterwards leave it 5
whereas it is not credible that the former
expectation (hould be ib much as half the lat*
ter. But I have a further reafon for thinking
that this calculation gives too high nuni«>'
bers, which has with me irrefiftible weight.
It has been feen, that the number of inha*
bitants comes out lefs on tht fuppofition,
that the defeds in the chriftenings are greater
than thofe in the burials. Now it feems evi*
dent that this is really the cafe; and, as it i«
a fafb not attended to, I will here endeavour
to explain diftin^i^ly the reafon which proves
it.

The proportion of the number of births m
London f to the number who live to be iq
years of age, is, by the bills, 16 to 5, Any
one may find this to be true, by fubtrading
the annual medium of thofe who have died
under 1 o, for fome years pafl, from the* an*
nual medium of births for the fame number
of years. — Now, tho' without doubt, Lon^
don is very fatal to children, yet it feems. ifH.
' credible

the State g/^London^ Population^ &c. 179

credible that it fhould be fo fatal as this itn«
plics.. The bills^ therefore, probably, give the
number of thofe who die under 10 too great
in proportion to the number of births ; and
there can be no other caufe of thi^, than a
greater deficiency in the births than in the
burials. Were the deficiencies in both equal ;
that is, were the burials^ in proportion to
their number, juft as deficient as the births
arc in proportion to their number, the pro-
portion of thofe who reach. 1 o years of age
to the number bom, would be right in the
bills y let the deficiencies themfelves be ever
fo confiderable. On the contrary; were the
deficiencies in the burials greater than in the
births^ this proportion would be given too
great ; and it is only when the former are
leafl, that this proportion can be given too
•little. — Thus; let the number of annual
kirials be 23,000; of births 15,700; and
the number dying annually under lOp
io,8co. Then 4,900 will reach 10, of
15,700 born annually; that is, 5 out of 16;
—Were there no deficiencies in the burials^
and were it £zQ, that only half the number
born die under lo; it would follow, that
there was an annual deficiency equal to 4,900
fubtraded from 10,800, or 5,900, in the
^r/Ar.— Were the ^/r/i6x a third part too little,
and the burials dfo a third part too little,
the true number oi births, burials, and of chiU
iren dyingunderio, would be 20,933—30,666

N 2 and

1 8o On tbi ExpeSlafion (f Lives j

and 14,400; and, therefore, the numbefr that
M^ould live to 10 years of age, would be 6,535
©ut of 20,93 3> or 5 of 16 as before. — Were
ih^ births a third part, and the burials fc much
as two- fifths wrong, the number of births,
burials, and children dying under 10 would
be- 20,933 — 32,20c — and 15,120. And^
thereibre, the nunvber that would live to 10
would be 5,813 out of 20,933, or five out
of i'&.-— Were the births a third part wrongs
fltid the bnriah but a 6th, the foregoing num^
bers v^rould be 20,933 — 26,833— -12,6^0;
«fui* therefore, the nuniber that woudd Hvq
to 10 would he 8,333 oiit of 20,933, or 5
out of 1-2.56 : and this proportion feems
as low als is confiftent with probability. It
id fomewhat Id& than the proportion in
Mr. Simpfori^ Table of London Obfervations ;
and much Ws than tlie^ proportion ia^ lh6
Tabic of Obfervations for Brejlaw. The
deficieflteies, therefore, in the regifter 6i
iirthsi nofuft be greater thajn thofe in the
icgifteo of burials {a) ; and the ledft imm^

(a) One obvious reafon of this facl is, that mne of the
iirths among yeivs^ fakirs ^ Papiftsj and the three den&^
minaiions of Diffintirs. are included ib ffae bills^ whereas
fMny of their burials are. It is further to be attended t6^
that the abortive and (lill-born, amounting to about 600
UnnuaUy, are included in the burials, but never in the
births. If ive add thefe to the chrtftenings, prdbfVtiig
the burials the fame^ the proporti^ of the born acoord--
mg to the bills, who htive reached ten for the laft fixtceii
years, will be very nearly one third inftf ad of five fix-'
iwttbi.

I her

the State of London, Populatioriy &c. 1 8 1

bcr I have given, or 591,580 is neareft
to the true number of inhabitants. How-
ever, {hould sjiy one, after all, think that
it is not improbable that only 5 of 16 ihould
live in London to be 10 years of age ; or that
above two^t birds die under this age; the con-
sequence will ftill be, that the foregoing cal'
cuiation has been carried too high. For it will
from hence follow, that the expeSiation of a
child juft born in London cannot be fo much
as I have taken it. This expeSlation is 20, on
the fuppofition that half die under 3 years of
age, and that 5 of 16 live to be 29 years of
iage, agreeably to Mr. Simp/on s Table. But
if it is indeed true, that half die under 2
years of age, and ^ of 16 under 10, agree-
ably to the billsj this e.vpedation cannot be fo
much as 17 (^) j and all the numbers before
given will be conftderably reduced.

Upon the whole : I am forced to con-
clude from thefc obfervations, that the fe-
cond number I have given, or 651,580,
though fhort of the number of inhabitants
commonly fuppofed in London , is, very pro-
bably, much greater^ but cannot be lefs^
than the true number. Indeed, it is in ge-
neral evident, that in cafes of this kind num-
bers are very much over-rated. The inge-

{o) This m»y be deduced from the obfervations in the
Uil EflTay ; and it will be there proved, that, in reality,
(his explication does not exceed i8.

N 3 nious

I S2 On the ExpeSiation of Lives ;

nious Dr. Brakenrtdgej 14 years ago, when'
the bills were lower than they arc now,
from the number of houfes, and allowing
fix to a houfc, made the number of inhabi-
tants 75^1,800. But his method of deter-
mining the {a) number of houfes is too pre-
carious I and, befides, 6 to a houfe is probably*
too large an allowance. — Many families now
have two houfes to live in.— -The magiftrates
of Norwich^ in 1752, took an cxadt account
of both the number of houfes and indivi-r

. {a)Y\i. PbiK Tranfaaions, Vol. XLVIII, p. 788,
In a paper fubfequent to thia, Dr. Brakgnridge teJIs us,
that in a late Furvey it appeared, that in all MiddUfix^
London^ fFeftminJier^ znA Souibwarkj there were 87,614
houfes, of which 199324 were cottages, and 4810 empty.
And he acknowledges, that this, if right, proves Landm
to be much lefs populous than he had made it. See
Phil. Tranf. Vol. L, p. 471. He does not mention how
this furvey was taken ; but moft probably it muft have
been incorred. — Mr. Maitland gw^s two accounts of the
number of houfes within the bills. One carefully taken
from the books of all the pariibes and precindts belong-
ing to London ; and another taken from a particular fur-
vey in 1737] made by himfelf with incredible pains. The
firft account makes the number of houfes 85,805* The
fecond account makes it 95,968. And the reafon of the
difference he obferves, is, thit many landlords of fmall
places, paying all taxes, they are in the pariih hooka
reckoned as fo many fingle houfes, though each of them
contain feveral houfes. See Mr. Maitknd^z Hiftory of
London^ 2d Book at the end.-— This, perhaps, may be alfo
the reafon of the deficiencies which, I fuppofe, there muft
be in the furvey, mentioned by Dr. Brakinridge, — It will
be obferved prefently, that the number of inhabitimts in
l^nd^n in 17379 was confiderably greater than it is now,

duals

the State g/'London, Population^ &c. 1 83

duals in that city, {a\ The number of
houfes was 7>i39f and of individuals 36^169^
which gives nearly 5 to a houfe.— -Ano-
ther

•

{a) Vid. Gentleman's Magazine for 1732, and Dr..
Short* 5 Comparative Hiftory of the Increafe of Mankind^ p. 38.
In page 58 of this lait work the author fays, th^t, in or-
der to be fully fatisfied about the number of perfons to
be allowed to a family, he procured the true number of.
families and individuals in 14 market towns, fome of
them conCderable for trade and populoufnefs ; and that
in them .were 20,37 1 families, and 97,6x1 individuals^
or but little more than 4^ to a family. He adds, that, in
order to find the difFerence in this refpei^ between towns
of trade and country pariibes, he procured, from divers
parts of the kingdom, the exad number oi families and
individualsy in 65 country pariihes. The number of/27-.
miiies was 17,208; inMviduah jty^'i/^i or not quite 44
to a family.-— In the place 1 have juft referred to, in the
Gentlerhan's Magazine, there is an account of the num*
ber of houfes and inhabitants in Oxford^ exclufive of the
colleges ; and in fP''oherhamptony Coventry and Birmingham ^
for 1750. The number of perfons to a houfe was, by
this account, /^\ in the two former towns, ana 5^ in the
two latter. — Dr. Davenant^ from Mr, £r'/r^*sObfervations,
gives 4>2^, as the number of perfons to z family for the
whole kingdom. See An EJfay on the probable Method of
making a people gainer ji by the balance of trade. — The num-
ber K>( familw in Rome \n 1740, was 32,158 ; of inhabi-^
tants 140,080 \ or 4.4 to z family^^^^ln 59 Dutch villages,
mentioned by Struyk^ the number of houfes was 12,005 i
of inhabitants, 45,888, or not 4 to a houfe. Sec Suf-
milih's Gottliche Ordnungy or a Treaiife in German on
the Probabilities of Human Life in diiFerent fituations,
population, &c. Vol. I. p. 233. — In the whole province
of Vaud in Switzerland., the number of perfons to a fa-
mily is 4^. See the beginning of the SuppLment.^^From
an account taken in 1770, it appeared, that the number,
of inhabitants at £^^</j in Yorkflsiroy was 16,380, and of
families 3,899* In this populous and opulent town,

N 4 there-

1 84 Ott ihe ExpeStatfon of Lhes j

thcr method which Dr. Brakenridge took to
determioe the number of inhabitants in Lon-*

don

ffherefore, the number of perfons in zfamilyy is only 44 '
And cbe number in each houfey will not be quite 5, fup-
pofing twery fifth houfe to contain two families, -^Y torn an
account witb which a friend at Shrewjbury has favoured
me, it appears, that in that town, in 1750, the number
of inhabitants to a houfe was 4^. — Very exa£|: accounts^
of which I (ball take further notice, prove, that in the
parifh of Holy-Crofi^ one of the fuburbs of Shrewjbury ^
and at Northamptonj the fame proportion is 4j to a
houfe in the former ; and 4^ in the latter. — In the parifh
of Ackworth in Yorkjbire^ the number of inhabitants of all
ages, in 1757, was 603. In 1767, this number was
728. The number of hovfes in'thc former year was 160 ;
in the, latter year, 184. In the town of Newbury in
Berkjhire^ the number of inhabitants, according to an
account taken in 1768, was 3732 ; and the number of
houfes 930. In the parifh of Speen^ adjoining to Newbury^
the number of inhabitants in 1757, was 1200 ; of houfes^
303. There are, therefore, in each of thefe three laft
places, only four inhabitants to a houfe. — In the parifh of
yfUwincile^ rforihamptonjhire^ the number of houfes is 96,
of inhabitants 402 ^ or 4^ to a houfe, — In I7S7» the inha-
bitants of Adanchejler were numbered, and found to be
19,839. Thev have (Ince increafed near 30005 and the
number of houfes is now, I am informed, 4860. In this
town, therefore, the number of inhabitants to a houff
cannot be above 4-|^. The fame appears to be true of
f^iverpooL^^-^lt feems, therefore, that five perfons to a
houfe may not be much too fmali an allowance for Len^
don^ but is too large for England in general. From
whence it will follow, that Dr. Brakenridge has likcwife
over-rated the number of people in England, In a letter
to George Lewis Scott^ Efq; puWifhed in 1756, in the Phil,
Tranf. Vol. 49, p. 877, he fays, that he had been cer-
tainly informed, that the number of houfes rated to the
window-tax was 690,000. The number of cottages not
fatcd^ b? addsy was xiol accurately known ^ but from the

j^cco^nts

J

the State g/'London, Population^ &c. 185

don was from the annual number of burials^
adding 2000 to the bills for omiilionSy and
fuppofmg a 30th part to dic'cvery year. In
order to prove this to be a moderate fuppo-
fit ion he obfcrves that, according to Dr.
Halley's Obfervations, a 34th part die every
year at Brejlaw. But this obfervation was
made too inadvertently. The number of
annual burials there, according to Dr. Hal-
ley % account, was 1174, and the number of
inhabitants, as deduced by him from hi^
Table, was 34,000 ; and therefore a 29th
part died every year. Befidcs 5 any one
may find, that in reality the Table is con-
ftru<fled on the fuppofition, that the whole

accounts given in, it appeared, that they could not ex«
ceed 200,000 ; and from thefe dat«, in coafequeocc of
allowing fix to a houfe, he makes the number of people
in England to be 5,340,000* Dr. Brakenridge has here
under-rated the cottages ; and the true number of houfes
in the kingdom in 1766, was 980,692. See the latter
end of the iirft part of the Supplemita. Call tbem^ hov^«
jcv£r, a million^ and the number of people in EngJand zni
^tf^aUs will be four millions and a half, allowing 4- to a
houfe \ and 5 millions, allowing 5 to a i^^i^.— -The for-
mer i^ probably too large an allowance; but the latter it
artainly fo. The number of people in Engird niay«
therefore, be ftated as probably not moriB than 4 millions
and a half; hut ceriaialy not 5 mill ions. "^T be number <^
h^ufis in Inland in 17549 was 39S9439. In 1767, it waa
4.24,046. (See the Gentleman^ s and CiiisM's jlmanack for
1772, by Samuil IVatfony Dublin). Let 44. be allowed to
a houfe, and the mimber of people in Ireland will be
1.908,207. And, if a million and a half are fuppofed
in Scotland^ the number of people in Great Britain and
iffhnd will he about eight millions.

number

iS6 On the J&KpiSlatkn of Lives ;

muttber born, or 1238, cjic every year; from
whence it will follow that a 28th part died
every year {a). Dr. Brakenridge, therefore,
had he attended to this, would have dated
a 24th part as the proportion that dies in
London every year, and this would have taken
ofF 150,000 from the number he has given.
Buteveli this muft be leis than the juft pro-
portion. For let three- fourths of all who
either die in London or migrate from it, be,
fuch as have been born in London ; and let
the reft be perfbns who have removed to
London from the country, or from foreign
nations. The expeStation of the former, it
has been (hewn, cannot exceed 20 years ; and
30 years have been allowed to the latter.
One with another, then, they will have an
expectation of 22^ years. That is ; one of
22t will die every year (^). And, confc-*

qucntly,

{a) Care fbould be taken, in confidering Dr. Halky*^
Table, not to take the firft number in it, or loco, for ib
many juft born. 1238, he tells us, was the annual me-
dium of births, and looo is the number he fuppofes ail
living at one year and under. It was inattention to this
that Ted Dr. Brakenridge to his mi (lake.

It will be fhewn in the 4th ElTay, that the number of
the living, under 20, is given too high in this Table ;
and from hence it will follow, that more'than a 28th
part of the inhabitants die at Brejlaw anniiaily.

[h) The whole number of inhabitants in Rvmixti 17439
was 147,476, and the annual medium of burials for three
years, from 1741 to 17439 was 6338. A 23d part, there-

forcy

the State ^London, Population^ &c. 1 87

qucfitly, fuppofing the annual recruit from
the country to be 7C00, the number of

tirtbs

fore, di«d every jear. See SufmikVs GottUchi Ordfttmg^
<}uoted p« 183.

In 1761, the whole number of inhabitants in the fame
town, was 157,452. The annual medium of births for
three years, from 1759 to 1761, was 5167 ; and of bu-
rials 7153* One in 22, therefore, died annually. See
Dr. Shorfs Comparative Hijlory ofthi Increafi and Decreafe
iff Mankind in England and feveral Ceunirits ahroady p. 59,
60. — In 1752, the accurate and diligent Mr. Strujk^ took
particular pains to determine the number of inhabitants
in Jmfterdam ; and the refult of his enquiry was, that
very probably it did not amount to 200,000. The an*
nual medium of burials for fix years, from 1747 to 1752,
was 8247. ^^^ ^^ 24^ therefore, died annually. See
Sufnukh^ ibid. — Ac Jm/ierdam^ there is a great number of
Jews, and their burials are not included in the bills.
There muft, I fuppofe, be other deficiencies, and an al«
lowance for thefe would, I doubt not, increafe the pro*
portion of inhabitants who die annually, to one in 21
or 22. — At Duilin^ in the year 1695, the number of in-
habitants was found, by an exaA furvey, to be 40,508,
(See Philof. Tranfadions, No. 261)- I find no account
of the annual burials Juft at that time; but from 1661*
to 1681, the medium had been 1613; and from 1715 to
1728 it was 2123. There can, therefore, be no mate-'
rial error in fuppofing that, in 1695, it was 1800 ; and this'
makes i in 22 to die annually. See Dr. Shorfs Comparo'
five Hijinj^ p. 15, and iJtw Ohjervatiom^ p. 228.— The
annual medium of burials for five years, from 1755 to
^7S9> ^^ Manchefler and Salfordy excfufive of thofe among
Diflenters, was 743 % of births^ 756. The number of
inhabitants in 1757 was I9;839. See Note, p. 184. Of
thefe at leaji 1500 or 2000 were Diflenters.. About a
24th part, therefore, died annually. But it Should be
confidered here, that Manchefler has increafed fo faft by
accciiiiins from the country, as to have more than doubl-
ed

1^88 O^ the Expe^attM of Lives ;

births 3 rimes 7000 or z i>ooo, and the iu^
rials and migrations 28^000 (which are all

high

cd itfelf fiiice 1717 ; and thtt the tSk& of iiicb an m-

creafe mud be to raife the proportion of inhaUuints 10 the
deaths^ and alfo the proportion of the hirtbs and weddings
to the hurialsy higher than they would pthervirifc be.— The
annual medium of hiirials in the pariih church and cha-
pels of L£EOs, from 1754 to J 768, was 758. The nusn*
ber of inhabitants is 16380. See Note, p. 183. One iu
214 of the inhabitants, therefore, die annually. — Thefe
fads prove that | have been too moderate in making only
I in 224> including emigraats, (odie in Z^Wo/i annually.

In 1 63 1 the number of people in the diy and Uif/ertits
of London was taken, by order of the Privy Council,
and found toi>e 130,178.-— This account was uken five
years after a plague that had fwept off near a quarter
of the inhabitants ^ and when, therefore, the town be**
ing full of recruits in the vigour of life, the medium of
annual burials muft have been lower than ufual, and the
births higher. Coiil^ therefore, the medium of annual
burials at that time, within the walls, and in ih/t 16
paiilfaes without the walls^ be fettled, exclufive of tbofe
who died in> fuch parts of the j6 panfoes without the
walls, as are not in the tiheriiesy the proportion dying
annually obuined from hence m^ght be depended on,
as lefs than the common and juft proportion. But this
medium cannot be difcovered with any accuracy. Graunt
eftimates that two-thirds of th<^fe j6 pari(be$ are withia
the liberies \ and, if this is rights the medium of annual
burials in the city and Ub^rtin in 1631, was 5,500, and
I in 23I: died annually ; or making a fniall allowance
for deficiencies in the bills, i in %1. — Mr. Maitkftdy
in his Hiftory of London^ Vol. II. page 744, by a la-
borious, but too unfatisfa&ory, in ve [ligation, reduces this
proportion to I in 247 3 and on the fuppolitioiis, that
this is the true proportion dying annually, at alltimesy in
London^ and that the deficiencies in the burials (includ-
ing the burials in Maryb:ine and Pancrafs j^mihi^) a«iounC

to

the &tate gf L^rtdon, Population , &ۥ 189

high fuppofi(ions)^ the number of inhabi-
tanu.will bQ> 224 multiplier} by 28,000^ or
630^000.

I will juil menliicm here one other in-
illane^ of.ojCag^ation on the preient fub*
jedc,

Mfrf Corbyn Morris^ in his ufeful Obferva^
tion^ dn tbi pa^ gr$notb andprefentjiate of the
€ity of Lofidom puWiflied in I7?i> fuppofcs
that no more than a 6oth patt of the inhabi-
tants of Londd^y who are above 20^ die evef j
year^ and fron> hence he concludes that the
number of inhabitants was near a million. In
this fvlppofition there Wja^s an error of at leaft
OM half< Aci^oi'ding to Dr. Hailty'f^ Tab^le^
it has beef» fhewn^ that a 34th p2itt of all at
2a find upwards^ die every year at Brefiaw^
In London^ a 2!9lh parl» according. t6 Mn
SimpfinC^ Tabk> and alfo according to all
other Tables of London Obfcrvations. And
in Scotland it has been found for many years,
thaf^ of 974 mini?fters and profefTors whofe

to 31O38 annually ; 'he dcterm!ne9» that th« number of in-
habitants within the bills was 725,903, in the year 1 737,.
* The ffumbcf of burrals nbt btought co account in thd
Mis iS) probabty, n^t^ much greater than either jyt*
Brakenridge or Mr. Maitland fuppofe it. I have reck-
oned it (o high as 6000, in order to include emigrants^
^nd alfo to be more fare of not falKng betow tha truth.

It will appear in the laft EfTay, with an evidence little
fhort of demonftration^ that, at leaft, i in 20^ die an-
nually in Lmdoriy and that, confequently, the number of
inhabitants, if the ocniflions io (he burials are 6000,
cannot exceed 601,750.

ages

190 On the ExpeSlation of Lives %

ages are 27 and upwards, a 33d part have
died every year. Had, therefore, Mr. Morris
ftated a 3Qth part of a]l above 20 dying
annually in London^ he would have gone be-
yond the truth, and his conelufion would
have been 400,000 lefs than it is.

Dr. Brakenridge obferved, that the num-
ber of inhabitants, at the tin^e he calculate
ed, was 127,000 lefs than it had been. The
bills have lately advanced a little, but ilill
they are much below what they were from
1717 to 1743- The medium of the annual
iirths, for 20 years, from 1716 to 1736, wa«
18,000, and of burials 26,529 ; and, by cal**>
culating from hence on all the fame fuppo-
fit ions with thofe which made 65^,580 to
be the prefent number of inhabitants in Lon--
don^ it will be found that the number then
was 735,840, or 84,260 greater than the
number at prefent. London^ therefore, for
the laft 30 years, has been decreafmg ; and
though now it is increafing again^ yet there
is reafon to think that the additions lately
made to the number of buildings round it,
aire owing, chiefly to the increafe of luxury,
and the inhabitants requiring more room to
live upon {a). It

{a) The medium of annual burials, in the 97 parlflies
within the walls was,

From 1655 to 1664, > 3^64.

From 1680 to 1690, ■ ■ ■ 3139
From 1730 to 1740, *— 2316
From 1758 to 1768^ .^*^ 1620

This

J

the State of London, Population, &;c. igt

It fbould be remembered, that the num-
ber of inhabitants in London is now ib much
lefs as I have made it> than it was 40 years
ago, on the fuppofition, that the proportion
of the omiiTions in the births to thofe in the
burials, was the fame then that it is now.
But it appears that this is not the fadl.-**From
^7Z^9 (the year when the ages of the dead
were firft given in rhe. bills) to 174a, near five-
fixths of thofe who were born died under 10,
according to the bills. From 1742 to 1752
three quarters: And ever fince 1752, this
proportion has flood nearly as it is now, or
at fomewhat more than two«thirds. The
omi(£on8 in the births, therefore, compared
with thofe in the burials, were greater former-
ly I and this muft render the difference be-
tween the number of inhabitants now and

This account proves, that though, fince 1655, LonJmi
has doubled its inhabitants, yet, within the walls^ they
have decreafed ; and fo rapidly for the laft 30 years as to
be now reduced to one half. — The like may be obferved
of the 17 pariflies immediately without the walls. Since
1730, thefe pariibes have been decreafing fo faft, that
the annual burials in them have funk from 8,672 to 5,432,
aiid are now lower than they were before the year i66o.
Ip JVeftminftit, on the contrary, and the 23 out*pariflieB
In Midilifex and Surrey, the annual burials have fince 1660

advanced from about 4000 to i6,ooo. Thefe fads

prove, that the inhabitants of London are now much lefs
crowded together than they were. It appears, in parti-
.cular, that within the walls the inhabitants take as much
room to live upon as double their number did formerly.
—-The very fame condufions may he drawn from an
examination of the cbr-ijlinings.

formerly

_ I

igl Oh tb^ ExpeSiation tf Lives i

foroierly ibcdewhat lefs confiderable ihm it
jBay feem to be from the face of the bills «
One reafon^ why the propof tion of the a-
raounts of the births add burials in the bills^
comes now nearer than it did, to the true pro?^
portion, may, perhaps, be, that the number
of Diflenters is leiiiened. The Foundling
Hofpital alfo nmy have contributed a little to
this event, by leffening the nuniber given in
the bill^ as n^ing died under i o, without
taking off any fr^m thfe births % for all that
4io in this hofpital are buried at Pancrajs
chufch^ which \A not within the bills. See
ikt preface to 3/ eolkc^on of the yearly bills
of mortality from 1657 ^^ ^7h^ inclufive^
p. 1%.

I will add^ that it i» probable (hat London
h now beeemc lefi fatal to children than it
was ; and that this is a further circumftance
^bich nluft redctce the difference I have
ihcrrtioned ; and which is Hfcewife nccclTary
to be joined to the .greater deficiencies m the
btrdiSt in order to accouftt for the very iifnaU
proportion of children whofurvived 10 years
of age, during the two firft of the periods 1
have ipecificd.— -Since ly^^^LmJm has been
thrown mere open. The ccrftom of keeping
country-houfes, and of fending children to
be nurfed in the country^ has prevailed more;*
Bivty particularly, the deftra^vi^^fe of fpi^^
frtuous liquors among the poor hai been
checked.

I have

-J

tbeStaN^honiKak,Populati$n^bcc. 193

t liave fbevsm that in Lt^ndon^ even in ita
prefect ftate; and aircording to the mioft mo^
derate c6mputkiont' half the number bbrn
die \aridcr rAr'te-ycztsi t)f age. In f^ienna un-
det tii>di In MUnibeJiety xxxyditifioe. In iVi^r-^
wic6f under ^K : In Nortbarnpfion^ ^unAct
/(?»^&V.-^fiut'itiaj>pears from Gri^««/'s (i) ac**
curate atcoUnt 6f the births, : wcdditigi, and
burialsfih x\\t^ countrypariCiefiffor 90 years;
an:d 4l(bi' from Or. 5^^r/'6 colltaion of ob-
fenra^riODS in hisi C^mpai-ative Hi/ilry, and
brs '"Trcatifc^ entiiicd, .ATifti; Ohfirvamns on
S^own and Country Bills of Mortatity-y-i\i2t in
cottn^ry villagf^s andpatiihes, the major part
Mvi to m$turd age^ >an(t even to mari^y. In,
the pttriih of Hofy-Crhfi (tf), in Sahp, it ap-
' -^ ' : - -' • , peart

k «

>(4V See ithe Tabhs at the cod of this wbrk v . .

f ^} See Natural and Political Obfervatiom on the Bills of
Mortality^ by Cape* yoUn Gikttmt^ F. R. S*— Sec alfo Mr.
DirboHit ftifieo-Thiobgyy ^: 174, where it appears, that
i^thA pariib of Ayhho'\f\ Northamptonjhin^ xYio* lYkt biriht
had buecn, for 118 yedrs, t€> the marnage^ as 6 to i ; jtt
ihe burials had been to the marriages only as 3^ to i»

(cy This pariflbeontains in it a village which is a part
tif the fuburbs of Sbrewfiury. It eonfifis of 1460 acrea
of arable and pafture land; befides 300 acres taken up
by hoirfsb and gardens. It is fix miles in 'circumference ;
Mf'ofwbkh Ties' along the banks of the river Sivem.'^^
1 mention thefe particulars to (bew, that it may be reck««
^ned a coun^ parilh ; tbo% perhaps, notperfealy fo^-on
account of its neamefe to SbrtwJhity.^^Tbt ch/ifleninga
ill it exceed the burials a little ^ and the number x>f in*'

O ' tiabitanta

r94 - ' ^V iS£iE¥fe^MtiiM :i^ XJws:i

peark from a curious ragiflir, wliidbt hM b^ea
kept %i the: :R.ev. Mr. Gorjucb^ ttv yicar,^
thaf, of 655 who have died there tf gll^agea
for the la^ 20 years» 32 x> or Dear ooe hs^^
have, K?ed to 30 year^ of age: Al>d, by
forming a: Table of Obfcryations from thi
Fegifter, ia ^e mantier which will .be de-^.
£;:ribc;d in the laft!£&]r> I ifind that a cbttd
jiuft bocn in. this pariih has ao expe<SUt«oji* of
53 years ; and.tbat» ia general, under tike age
d£ 50, the expeSationt of lives here expeed
ikiot^Yxx. London^ in th? pfopoction of: about
4 to 3. — :Ijl the i^^QokM AckviQTth^ Tbr^-
jiEttrr, menttoQied in the note, p. xS4# il ftp-9
pears, from an exadfc account kept. \xf^ £>r^;
Let^ of .the a^^ at v«:htch all died, tibor^ Im
20 yearsii or from 1747 to 1767, xh2Ltbalf
the inhabitants live to the age of 46 — In the
province .x)f^f'ii»/i SvitzerJanJ, coa&Sdt^pf

,» . ' ' ' '

babitaots (mofil; labcHiring people) h^fi, for the laft- %0.
jears, kept tvTarJy! to 103O) without any cgiifid^rjitfle 19^.
crcafe.— The regiftcr of this parift from 1750 X9^ IJ/^Q^
)|as be^n publiflied in the Llid voLMoie ofxh^ Phttff^ncal
Tranfa&m^ PsMt X. Art. aj- AihJ 9i^.oji|:|nii||^iMof ^
from 1760 to 1770, has been lately communicated and
ifea4to»th&. Royal .Scxriety. It iii.k-ept wkh paxticu^
care and accuracy by Mr. Gnfucb ; and furniihes very^
ufeful daia >for determimng the difference in value bo«
't)¥een town andi country lives.^Ic deferves to *b€ men-i
tiontd particttlacifrt that no.firfigwnt or jir^m^ wfan
bappeiLtodie.iaLtb^ p^irifli^ or wbo^<9ay.t^>ro«igbt:int4
it to be bttriedv are pnjcered into th,Q regifter r Nor U9k
my of. the &x€dlii)ha^i£ant« ocmuedt thto' oarrM o«t <ft
be. buried*: .-*:...-.,. :• ..»

I- . J • ^ ii2»95i

the State ^London, PoputattM, &:c. i^^-

M 2,951 johabitants, half lire to 4i.«^Sd
gretc 18 tbe dtffirrence between the doratioa.
of human life in tewm%tiA in the country. ^^
Further evidonce for the truth of this ob^
fervation may be deduced from the account
given by Dr. Thomas Heberdttii and publiihf«
ed in the Phildbphical Traniadions (VoL
LVH. p. 461), of tbe incfeafe and mortality
of the inhabitants oj. tbe ijland of Madeiras
In this iflaad, it feems, the weddings have
facsen to the births, for 8 years, from, 1759
tor 1766, as 10 to 46.8 ; and to the burialSf .
as 10. to 27*5, or 9 to 24.75. Doubieiheie;
pro|)oition0, therefore, . x>r the proportion of
ao to 46.8, and of 18 to 24*75, are the.
proportions of the m^nber marrying annu«»
aUy, to the number born and the number,
dying. Let one marraagein three be a 2d ot
{a) 3d marriage on the fide of either the man
or the woman ; or, in other words, let one in
fix of ail that marry be widows and widowers 3
and 9 marriages will imply 1 5 perfons who
Have gpwn up to maturity, and lived tOj
marry once or oftener ; and the proportion^
of the number marrying annually the firft
time, to the. number dying annually, will

be 15 to 24.75, ^^ 3 ^^ 5* 1^ Q)ay feeaxi ta

• • • •

(a) Thjs proportion is taken from hSt.-^lti all Aw^-
raniaj during 9iyear8, from 1748 to 1756, tbe number of
perfons who' married was 56,956 ; and of tbefe^ 10,586
west wi Jotvs znd whkwers. SufmikVt Works, Vol. L
Tables, p. 98. .

O % follow

1^6 On the ExpeSlatUn of \ Lives ; / .

follow horn hence^ that in this ifland tbree-^
fifths of thofe who die- havr'bcetiiinarriMl;:
and, confcqucntly, that only two^fifths of che>
inhabitants die in childhbod rand ceUhdcy.;!
and this would be a juft conclufion weie:
there no increafe, or had the births and bu-
rials been equal. But it muH be remem^f .
bered» that the general effedil of an inciteafe
while it is going on in a conntry, is to rerii*:
der the proportion of. perfons . marrying an-
nually /to the annual deaths* greater y and to/
the annual l)irths Jefsi than the true prbpor^
tion marrying, oat of any given . number
born; This proportipn geiienally lies, her
tween the other two proportions^ but alwajts
neareft to the firft {a) $ and, in the prefent
cafe^ it cannot be fo little as one half. .h^\
greeably to this, it appears alfo from Dr.
I Meter den* %]

{a) In a country where there \% no incr^a(f» 9r>dc<f'
creafe of the inhabitants^ .and where alfo life, iq its 6rft
peViods, is fo (lable, and niarriage fo much encduriage<f,'
that half of all who are born live to be marriedj^h^ «»-'
nual births and burials muQ be equal, and alfo quadruple.
the number of weddings, after allowing for 2d and 3^
iharriages. Suppofe in thefe circumftances (every thing
cHe remaining the fame) the probabilities cfli/e^ during^ tes
fkft ftages, ta^ improved... In this cafe^ more Am\,baif.
the born will live to be married*, and an increafe will take

Elace. The^ births will exceed, the burials, and both f^U
elow quadruple the weddings ; or, which is the fame,
below double the number annually married. — Suppofe
next (the probabilities of life and the encouragement to mar^
riage rcmainihg the (ame) the prolifcinefs only of ^hci

i

mar-

fie State if-Lon6oii,Popul^t$oti,6cc. 197

Heier^kn's accottnt, thit the expeStathn of a
cliiU: jtift bornan Madeira is about 39 yeanB ;

9
or

Ikiairviages to he improvfd. > In this cafe it is plain, that
an increafe aJfo will take place ; but the annual h'wihs and
burial^) inftead of being Ie(s, will now both rife abov«
'^uadhiple the weddings; and therefore the proportion of
:tbe,bofn to that part of the born who marry (being by
^uppofipou two to pne) will be lefs than the proportion
of either the /7n;zW births or the annual burials, to the
Vtumber marrying annualfy,*^St\i^^oh again (the encpumgi"
Aliens ta marriage remaining the fame) that the probabilitiis
joflife and the proliJUkmfs of marriages are both improved.
\t\ this cafe, a more rapid increafe will take place, or ji
greater exccfs of the births above the burials ; but at the
fame, time they will keep nearer to quadruple the wed-
clings, than if the latter caufe only had operated, and
jproduced the fame increafe. — I (hould be too minute and-
tedious, were I to explain thcfe obfervations at large. It
Mlbws from them, that, in every country or fituation
where, for a courfe of years, the burials have been eitbef
tqual to or kfs than the births^ and both under quadruple
\he marriages ; and alfo that, wherever the burials are
lefs than quadruple the annual marriages, and at the fame
time the births greater^ there the major part of all that
are born live to marry.

I have fhewn how the allowance is to be made for 2d
and 3d marriages. Very wrong conclufions will 1^ drawn
if this allowance is not made. Btit it is, in part, com.-
penfated by the natural children which are included in
the births, and which raife the proportion of the births
to the weddings higher than it ought to be, and there^
fore bring it nearer to the true proportion of the number
horn annualhfy to thofe who marry annually, after de-
du<3ing thufe who marry a 2d or 3d time.
, In drawing conclufions from the. proportion of annual
births and burials, ih different fituations, fome writers
on the increafe of mankind, have not given due attention
to the difference in thefe proportions, arifing from the
different circumdances of increafe or decreafd among a

O 3 people.

s

I

798 : ''On the Expe&Mlm af Lives t

'or more than double the ezpfa3atioa bf t
icfaild juft born in London^ Por the nucihlficr
iOf inhabitants was founds by a furvey made
in the beginning of the year 1767, to tic
64,614. The annual medium at buridb
liad been, for eight years, 1293 ; of birthi
220 1. The number of inhabitants, divided
by the annual medium of burials^ p^i^^
49.89; or the expectation nearly of a chift
juft born, fuppofing the births had beea
1293, and conflantly equal to the buriah^
ihe number of inhabitants remaining the
Xame* And the fame number, divided by
the annual medium of birtbSf gives ^9.^5 \
or the expectation of a child juft bom, <up*
pofing the burials 2201, the numb;crof births
sind of inhabitants remaining the fame. And
the true expeBtation of life muft be fome-
where near the mean between 49*89 and
29,35-

people. One inftance of this I have now mentioned ;
^nd ope further inftance of it is neccflary to be mentioned.
The proportion oi annual birtha to weddings ha^ been
iconfidered as giving the true number of children derived
from each marriage, taking all marriages one with ano*
ther. But this is true only when, for many years, the
births and burials have kept nearly equal. Where
there is ap excefs of the births occafioning an increafe^
the proportion o^ annual births to weddings muft be lefs
(han the proportion of children derived from each mar-
riage; and the contrary gjuft take^ place vv^here there is a
dc(:reafe»

. Again:

Again : A 5Pth ptrtof the.ioiiftfciMdts of
iUbkkirn^ it appears^ die anfiually. In Lon*
tisMf I have ikewn, thtc above twicfe this
^oportiondies anmially. In iebaUer. towm
a fmaller propdrtioB dies {a) i aqd the \sinht
aUb come nearer to the buritls.H^b gewral i
there feems reafbn to think t&at iatowo^
(aUplviflg for particular advantages. of &tda«
tioo^ . trade^ police, cleanliness^ ahd , opeiirr
ncfs, which fome towns may have,) the ex-
ccfk of the burials above the births/ aAd the
|iroportion of inhabitants dying anliually^
are, more or lefs as the towns are greater or
iioQaUer. In JLomion itfelf, about 160 years
ago, when it was fcarccly a fourth of its
prefent bulk, the births were much nearer

(is) In LmuUn^ thi« proportion is, at the higheft, i in
-aoj.— In Ngrwich^ 1 in 24.4. — In N$rthampt9n^ i in 26*.
See the laft Eflay. In the parifli of Newbury^ Berks^^
confifttng of 3732 pcrfons, all town inhabitants, the an*
mial medium of dheaths for 19 years, or from 1747 to
1765, has been 136. In this town, therefore, i in 27^-
die annually. The contiguous pari(h of Span coniifted,
in 1757, of X20O inhabitants, about 520 of whom were
inhabitants of that part of the town of Niwbuty which is
in this'parifh, and the reft were country inhabitants* For
34 yeaxs, or from 1724 to 17579 thirty-nine died here
fiMotalfyi or I in 31.— •In both thefe parilbes the births
and bi^iah are. nearly equal. — I believe thefe fadb may
l^c depended on^ and th^^y feem to (hew us tery di*
ilinffly the gradations in the degrees of human truyrtaliiy
irom griat towns to m^^^/f towns, and from ^^^d^^Ar
towns to Jmall towiis, and to parifties, conltftrng partly
of town and partly of country inhabitants* The* Aext
note will ihew what the dcgr^ cf hui^ian mortality is in
places purely country.^ »

O 4 to

- ^«^

aeo On tii E?cpeSktiidn (^J Liwi ;

40 th» buriiUs, tlnan thej^- »cnt>Wi'fBtit
in cowiitry: pariihes ^atnd laHages, the biitAft
almoft always -iexteed 4ht . buriah $ and* -^
believe: it iieldom happens that more lbM|
# 40tli (4) part of the mbabitants die an*
nuallf . In the four provinces of New^En^
iand there is a very rapid increaie of^ 'the
inhabitants; hut, notwithftanding thiSy at
Bafhn^ t)M capital, the inhabitants ' vMuld

{a) Accprding to Graunfs account x)f « p«d(h ia Unaf^y
Jhin, not reckoned, he fays, remarkably healthful, a 501^
part of the inhabitants had died annually for 90 years.
Natural and Political ObfenMtidnsy bfe. Chap. xii.—In the
pariih of Aekwartb already, mentioned, one of 47 die an-
nually. In the province of Vaud^ Switzerland^ ope 111.4^
die annually. See page 195, and the (irft part of the Sup*
pkment. In 1098 country pariflies, mentioned by Supmlchj
the annual average of deaths, for fix years, ending in
1749, was 5255. The number of inhabitants was 125,3S7*
One, therefore, in 43 died annually.— ^In 106 other pa»>
riflies, mentioned by him, this proportion was i in 50.

In the dukedom of Wurtemberg^ the inhabitants, Mt\.
Sufinikh fays, are numbered every year \ and from the av<«-
rage of five years, ending in 1 754, it appeared that, taking
the towns and country together^ i in 32 died annually.'—
In another province, which he mentions, confiftirig of
635,998 inbaVitants, 1 in 33 died annually. From thefe
fads .he concludes, that, taking a whole country in grofr^
including all cities and villages, mankind enjoy amrtng
them about 32 or 33 years each of exiftenoe. And dits,
very probably* n^ay not be far from the truth in the pre^
fs:nt ftate of moft of tha kingdoms' of jEvrv/^. And it will
follow, that a child .born' in a country pariihor village,
has, at lead, an expedation of ■36*0^37 years ; fuppofing
X\\c proportion of country to ipwu inhabitants to be as 3^
to I ; whlch^ I thinks this ingenious writer's obfervation^
prove- ^Q he nearly the cafe 'xhPmirania^ Brendenburgh^
and fome other kingdoms.

,: dccreafe

the $tt$t^yiuoxAaiif'Ih^lathn^ «of

.^oereafer were thettT no fupply froth Ithe
i^rottttiry. : for^ if die account 1 htve feen 'is
|ttft, . ffom. 1 73 1 to i ^6s» the barbds all «u-
j0Bg QKcecdi^ tlKt births (^?). So remttfk&falj
iio^toiynsy in confcqucoce of their onfavoar^
ai>kfiei$ to health, and the loxQry which
^generally prevails in theflHf check the increa&
*fif .ce«ntries«

. : . Jjdalthfal nefe and < prdifickneis- arct pni«*
j)0bly» t:auies of incrcafe feldom feparated.
In copformtty to thi? obfervation, it appears
from comparing the births and weddings,
m countries and towns where r^iAers of
•them ,have been kiept, that in the fbrmer,
carriages, one with another, feldom pvoduce
iefs than four children each ; generally he-
-cween foar and five, and fometimes^tibove
iiv*. But in towns feldom aboveibur^ge^
nera^ly. between three and four; ^nd ibmc-
4iflifiS.uiicier three (^).

4

(tf) Se& a particular account of the births and buriafs
ii> this town from 1731 to 17.52 in the GintUmaii s Ma^

'^aii/ii for 17 S3^ P- 4>3' ' '

i •. • . • . * . ■ ■

,. it} Any one. may fee what evidence there is for this,

^y confultihg Dr. Short\ two books already quoted, and

[<)att,AiridgmiM cf the Philofopbical Tranfa^iens, Vol. VII.

.f>a(^W/|li( ^f ^MGrawtt^s acpQunt already <ptoted) of the

births, weddings, and burials in three country pari&es for
.^o years ; compared with iimilar accounts in towns. In
. (^on£.derinjg thefe accounts, it (hould not be forgotten

that allowances muft, be made for the difterent circum*

Ranees of inck^afe or decrcafe in a place, agreeably tp
Hhe obfervation at the end of the note in page 196, >

; ^ I have

.- I

tot t^ tie E^Bstkn ^tA¥ni

I hmt fdoMtimes lieard tihe ^cat inmi^
lier of. old |>eoplc.in i^^?^/?^ menciMicd^
to prove its favoorHbleners to health and
l6Ag life. But no ob&r^ation can be flowre
<rronco«.. There oaght, in nealityt to 'be
ixMtc old people in London^ ia {)ro)>i^aQii to
the number of iflfaabitants, than in ^mf
iinaller towns ; becaufe at leaft one^i^vorM:
of it$ inhabitants are perfbns who come ia-
to it from the country, in the moft ^roboft
part of life, and with a much greaiter probft-
bili;ty of attaining to old age^ than if they had
come into it in the weaknefs of infanqr.
But» ncAwithftanding. this advantage, there
are much fe^hrer perfons who attain to great
^igfes in Jbondorif than in moft oth^r. places
where obfervations have been made^^^^At
Srefiaw it appears, by Dr. HaMey*s Tables
that 41 of 1238 born, or a 30th part, live
to be So years of age. . The fame, I am in^
formed, is true of Manchejier (tf).— In the
|)ari{h of Att-JdintSy in Nortbampion^ an acr
count has been kept ever fiface 1733 ^^^^
ages at which the inhabitants diei and I
find that a 22d part die thcfc turned of 8q*
At Norwich a like account has been kept^

and it appears, that for the laft 30 joeara, a

-I , ...

(d\ Tbe account I have here given of Manchejiir^ and
'alfo in page 193, 187, 184, I owe to the information of
Dr, Percivaly a very ingenious arid able phvfician in this
'town, and author of the EJfayi Medical and Experimental^
lately puUilhed.

I 4 27th

the Sme 'tf/'Loniidh, PifukfwH.tce. ^d%

%^ part 'of die inhabitants hweSiid, tuirn^
«d cff the ftrtie ag6.--^— -Acoordihg to Mr;
M^ffebcofris Table of Obfervations, piiMift-t
fed at the end of the third edition of Mr. Dt
^Mofw*e*sTT€^tifc on l!hfe DoSrine of Chaiitfcsi
at i4/i&'part di!e turned of 86. And l^h is
the very proportion that died ttirhtd of 8x>
ia 4he parifli of AckwortB, for the 216 Jrefara,
imentiohed page 194. In the pariih of
Hoiy^Crofs^ already mentioned, p. .18^4 an^
p. 193, the eleventh part of the inhabitants
life to Bo {a). See Table III. Supplfthtent.
•i^-^Btit in London^ for 30 years, ending a<t
'<heyear 1768, only 25 of every 1000, who
lii^e died, or a 40th part, have lived t6 thi^
ftge ; which may be eafily difeovcWd, by di^
viding the fnm of all who have died during
thefe years at all ages, by the fum of all who
have died above 80.

Among the peculial- evils to which grcil
tovsms are fub}e£t^ I might further mentidh

{a) This, however; wiU appear itfelf ineonfideriblet
wlien compared with the following account : ^^ In 1761
^< the burials in the diftrid of Chrijiianna^ in N9rway^
^* amounted to 6,929 and the christenings to 11,024,
*< Among thofe who died, 394, or i in 18, had lived to
** the age of 90 ; 63 to tbe age of looy and feven to the
.^^ age of .io|.»^In the diocefe of BergcH^ the peHbnt
'^ who died amounted only to 34580, cff w4iom t8 livei
^^ to tlie age of 100 ; one woaan to the age of 104, ami
^^ another woman to the age of 108."

See the Jtnml Rtgijltr for 1761, p. 191.

the

the PcAffit^^ Ei«fe«!«?rJbfi y4»^oiii*66,;:|lMf
dFoad^l. {^^^Sjfi\%j laid London a^i^dft wa|^f
jQ^i^eiP c^Wfy 15 or ^0( years i %nd there i^
Aq r^ft)n';9, t|iinJt,:.that it was xm g^pgrajly
b^rwiiM itfelf, :A »V?A happy, aiteratiufi
ha^; %k^a .place ; whichi p^rhaps^ in part ^
mm^ M^. S^^ grpa^cr a^y^antaees ^f cleanjir
n^j^and qpenneiisy which London \i^i^v^pi
ilncgiit was rebuilt;. and which lal^ly h^
jp^jfn^vcry jw^ifcly inapr/oyed. \ .,

, ' : . • » • , . .,

.# ^-* ....l.n '* • • .'J

^ ;The jfafft$ I have now taken notice .of 4if
ib ifnppr^nt that> I think they def^^irve qiore
attQhtion tWn has^ been • hitherto • beftow<sd
;Upoi;i « t^em. Every one knows : thi^t tiit
ilrjei>gtb of a ftate confiAs in the nun^ber of
people. The encouragement of pppulation,
therefore,, ought to be one of the firfl ob«-
jcdts of policy in every ftate j ancl ibme of
the worft enemies of population are the lux-
Aiv.yr (^ ^centioufneff^ and debility pro^iiced
and prqpagated by great towns,

, : I. have obfervcd that London i;5 now (^ )
increeifing. But it appeafs, thatj ifi tfuttf,

•; . ' ' , ... . thw

{a) iTikil uacreafe. b gteatcc than the. bills (bewi, on
4QCoufitfif'tl)eomiffion in them of thetwopari(he5mibic)i
liavi been cnoft increafed.hy .ndwr 'butMings:; I meaft
'Morsi^eii3Ln6.P»ncrafs.^as\ms%*. :Thjr former of theft
pariihes is now ohe of the iacrgeft in London. ; Xhoan^
nual mediuin of burials ^n Tt for the lad 10 years has
bctSi^732.— In Vancrafs pirJfli Vhfe medium, for the Cime
• S time.

the Stati 6/Lpnd(M',P9^Ja^n/icc. 1I05

t}m b an evcBt titofe to 'bie^ dr^dUid ^tiian^de--
£«eii; The more* jLrc»ff^itifioreafe0^&e.morb
iht reft -of th6 kingdom itiuft be defected;
fbe^fevtrtt hands mtift be Mt fora^ioakure^
and f con&quemty j^ tits • kfs • mixft be !tkei|sliso-«'
ty\i^$ktd Hia hrgh^P'tHe prrceofialKtheiiittaiift
c^ fbbiiifeeiice.' Moder^e townrs» Imngf feats*
tof) riribfimttient, emulaticn, . aiidt artt^ r nkayi be;
)iifUk advsintage6:i But ^rn/ tcoi^as;. liicmg.
befons^ tfaey grow to'half thefbutio oiLmA^^.
bacotxie-clseckis on population 1 of -too hurtfur
H natore^ ncrrferies. iof ddsfuv^heryl and volup^*
tiiotffnefs $ ^^nd^ - in ' oMny ' refpe^^a, greater
arils tfaanfi^cda iieOcdmpehfated fajrany-iui^.

V«liagei (a)* • I ^ r.s .-...l .;;: ' , rtj.;:..; •♦

time, has been 309.— *lt will, perhaps, be a lattsfadion
tofo^Qi^lto be funher^jnforfni^;tbat, from an accurate
ac9puiit taken in March jj^jZy it appeared, that thenumt
bcpbf Tn^abitants in'that part of ttus laft'parifll wWph"
joM %lo Lmdon was then Jfjgf oi whom ij;94 ^iie
kdgvs^'f and tha): tbc^number of h^Jls was 47i&,.of whiph
about 330 have been built wJthiA thefe feyfcn years.-^t
will'bfe obferved here, that, in this part of Pancraff pa-
xAz there-'We above f«vcn tierfons. to a houfe i but it
fliould be obferved likewife, that it cbnutts chiefly of
lidgln^hmfiSj *and thaCT tM liC(50Qnt was uken at a time '
of the year when it Was 'fvXMt of lodgers ; and tha^ eon* •.
fSquentty) no-canckifiiMveaA be drawn finani hence with
refped to the proportion of inhabitant* talioulbs7iii: '
^ in general.

s :j^

.. {a) The mean apni^f^I hirihs^ ived£ngs^^ 2LnAbur(als in .
the .following towns, fqt fome of the laft years, have been

nearly, . / 1 . : . •

At

tfaeinhaboanta cbuhto tiicic ovratiiUmbtir jn
^{4 3iQar8. fiat this (as. ygOh Sit» imlUkoow^
]$ a weiy ifloWi iaoceafe^. comptred . witli tkafe
iviiic^. takoi place among our ^^obiitf^ n
Amskioa. : In tke baokifcttlemcoCfi, .whem
the. iohfiSMlapts apply ^eJnielv.e8 cntkety< tfit
agricukui^^ . axid; 1 i^^ory . ia . not . koowity chefo
^j^niblQ their own niu&bci: in r5 years ;atad(
s41 thra' tbe ndctfaern <taldraes» in 25 yt9Lvm{a).:
Ithss i& an)inAanoe:€if. increafe .£>xapid^ ae tot
hajvfi fbaacely any/ pimalkl • The bic lbs . in;
diefe xoiimtctea mitflr:; exce^dr xhfi . buriak;
mncl^imQpB duoa.aa^ .Mt^^iroi^^iafidfa.^ealat'
proportion of the born mufl reaph matttob^/
tyi-^In 17389 the number of inhabitants in
New Jerfey was taken by order of the go-

I< t «w<l < I . •• . . •< » i, // I 1 -» • • ,' ^•^'^ '3

■ ' Births. • ' Weddings-. Bbria!»;

■ %iX^, \ ^ - „ , ■ - ■'•*-•

AaifterdAniy -—4,600 ^r- '2,460^ — '8,ppO
Qopcnhagrn^ — 23706 -^^ 886/ — 3>30o

It defervM notkc, that before ipjCbt tJI that died in . tbe
ko^^k it'fdemo were omiMtfeisv, the; btiUe.— OC#ie
Poriif Ulb-JLflMre particuUr acocnuH wiU bcrgivpni^'tl^f
Poft&ript^tiLtUsoEffiiy..

•J' 1 .*.,' <

(tf ) See a Dircourfe on ChriJHan UnUn^ by Dr. Siyliiy '
Bffivty I?^!* P* ICU- l09,,&9,-7-Scc alfo, TA^ InUreft of
Great, BriUfin cwfider^d with regisjri i$ her Cehnies^ tojptmr
with Ohferi>aMm concetTting the liter eaje ef MmHnd^ peirpUng
§fCountri$Sy &c. p* 35. 2d edit. L^ndorij 1761.

vernmenty

the S^0U^^ft^vAtm% Jp^^^ £07

Hriiisf«ntft aAd (pwA^iQ ht 479369^. &vca
jr^ira a6er¥i:ar<i«^ tb« iwimber c^ mfaaihitaals
wa3 ag«U> t^ea i ited, foimd to W iiumafed#
bf jiroctfutioD onl7» ^boM 1 4^000.1 ^and imyf
Vis» 9iOQ:i4^ofr ^e inhabttaata fimefiilind
to be under (/?). i 6. yMC9 of age. {ne2i^'yi^,
tbcrcComi they nu^ hftMC.doubkd thtir^^vwii
niimb9i:» and the.bktha^sauft bavc ^^arcetded
tbebwitls i^QOo 4iQiiutUy« Aa iho ioamb
bere is. rawh qjakker than in Mmkirai wo
may be fure that a fmalfer proportion of the
inhabitants muft die annu^ly* L^t iis^
however, fuppofc it the fame, or a 50th part*
This will make the "atihual burials to have
beepc during thcfQ.feven years, iqqq^ apc^
the. anooatl births. ^00^, or aa i9th paat of
the inkabitants.-~Sith¥lar obfervattons ^lay^
be rftade on the . much quicker iiicreaie^
RAoiie tfkmd^ as rdated ip the p«e£M:e to«thc
ColkBkn of the hmdm Bilk ofM^rtiil^ % and
alio in- the valuab^ pamphlet laft qupdcdvOn
the Inter efi cfGreflt ^ritijJifi witkiregmd t^ iiit\
CohnieSi p. 3 6.-^ What a prodi||ioQ6 differ-
ence muft there be, between the vigour :^n4
the happineis of hui?;ian life in fuph Jijtti^*!
tions^ and in fuch a place as Lmdan j^«^Tha
original number of; perfons ' who, tni 16439
had fettled in NcivrEngIan4$ wais zi,^ppj
Ever iince, it isjiockoned, that more kbro

^ *»

(fl) According tp Dr. Jf^Uy^s TM% il^c nvnplitip rf
the lirifl^ Hpdcr l6j is 4>ut a| thfrd of a}] the living ^t .^

left

left them <(han iM!(re^lMi« tt> «t^^ In

tk&yeariiydb^ ^tfaiey^wereijncreafed Id-hdf a
ihittioiu: ^h^y hiivt, > dierefore; all along
dotfbfed tbeir^wn minibc^ in 25 year^. And
iiFthay-coiTtiiiue'to ihdreafe) at the &nne> i«ce;
tlwp'MQUyr.^o.yeari hence/ in Ne&^Efig&nd
alone'i^ibe four 'milKons y and in alt Nortib
Americai above 4wke the number ofe Inliabi-
tants::m Ghtat Britain (^).«— But I am wann
dcring iit>m' my purjpofe In diis letter. The

• tJ 4* 1. .ii»i- . ^ .- - » ^H}1IK

' :; V*-Tx -A / '•• - ''"- ' ■ *'''•*' • •' •

, \fy, Sf^ Dr. Ary^/s pamphleCy juft quoted, p.aiQ» &c^:

(i)' The : rate of incrcafe, Aifpofixijg the.procreatfve
powers the fame, depends on two caules : THe'*' encou^
•• rageitieiit to marriage i** irfd the ^« ixpeSiaU^6f t chili
cvytift.bbiai/' I When oner of there Is given(, thtt incr&dS
^»(Vi« ;^?KW. )»J>^t>porfi<iii t9i tte^ther, ijhit .$i ;• A>
mucn-j^r^^/^l-or /(j/J as thft ratio is of the nunfit?^r^ who
^klf tnatirttt^,*afnd'orAoft whd mari'y, W ih^ numbiKj!
tor*, Al ititich ^cJUr^rJbwir* will he the tndre^fe.— s-LA

¥AfSI^^J^<^^^»o^ ^ l*^«fe c^wft« M^% aat6.i?roduc(|
^(1 annM^l e^efe pf ther^j^/i&j.a^pve the Mr^i^^ j^qu^l to a
36^' t^alt of "thVJ ^whble nOrnbef of mhabltants'. It riiaj^
ftetti tb'%>Uoyir lYom b&kceV that the mhabitants wdti}d
dm^ ^|herr .c«i!6 mtmbpr ^jn ! 36' y«ars ^ and ( bia .&ine
have calculated: But'th^.uutsh is* that theyVould dou-.
e their own number in much ieis,ttaie. . Everj addition
tb* thenmimbe^ of tnhabrtaliti^nrthe'bfiths, produces i
pr6iiMM^aUy/grdliter;noMabfcr of ibirths^ ^aoda: gt^mt
excels pfptbete above tbe^ burial}^} and 'if we;fut>]>ofe th|;
ixdels to increajTe annuall^ at^ the-fame rat^ with tn^ in-
habiftints; o^fe as;to prerfifWVthrrtf2[/Vof ifwthe'num*;
ter^ billidlttaliti'ilways.:the.>ainei ahd tOair )iihi» r/r/d

p the period of doubling will be^ the quotient produced

by dividing the logarithm of :& by thc?>^!f^r/ff<^ 'betwecR
the logarithms' <if r '+ t and* r i is "might' be wfily de«%
pnonftrated. In the prefent cafe, r toeing 369 and r'-^^
• being

f be Sfafe of London, Population y &c* 209

point I had chiefly in view was, the prefcnt
ilate of London as to healthfalnefs, number

of

•

betog yj^ the period of doubling comes out 25 years. If
r is taken equal to 22* the period of doubling will be 15
years. — But it is certain that this ratio may^ in many
utuations, be greater than -^'^^ and, inftead of remaining
the fame, or becoming lefs, it may incrtafe^ the confe^
i^enca kA which will be, that the period of doubling will
be Ihorter than this rule gives it.— According to Dr.
Halleys Table, the number of perfons between 20 and
42 years of age is a third part of the whole number living
at all ages* The prolific part, therefore, of a country
may very well be a 4th of the whole number of inhabi-
tants ; and fuppofing four of thefe, or every other mar-
riage between perfons all under 42, to produce one birth
every year, the annual number of births will be a i6th
part of i)ie whole number of people. And, therefore,
fuppoiing the burials to be a 48th part, the annual excefs
of the births above the burials will be a 24th part, and the
period of doubling 17 years. — The number of inhabi-
tants in Nev^'England was, as I have faid from Dr. Styles'%
pamphlet, half a million in 1760. If they have gone on
increafing at the fame rate ever fince, they muft be now
640,000 ; and it feems to appear that in fadt they are now
more than this number. For, fince writing the above
obfervations, I have feen a particular account, grounded
chiefly on furveys lately taken with a view to taxation,
and for other purpofes, of the number of males, between
16 and 60 in the four provinces. According to this ac*
count, the number of fuch males is 218,000. The
whole number of people, therefore, between j6 and 60,
muft be nearly 436,000. In order to be more fure of
avoiding excefs, I will call them only 400,000. In Dr.
flalley^s Table, the proportion of all the living under 16
and above 60, to the reft of the living, is 13.33 to 20 ;
itkA this will make the number of people now living in
the four provinces of Ntw-England to be 666,000. But
oa account of the rapid iocreafe^ this proportion muft be

F con-

a I o On tie, ExpeSifltion of Lives j

of inhabitants, and its influence on ppp^^^
tion. The obfcrvations I Have made imy^
perhaps, help to (hew, how the mod is to be
made of the lights afforded by the London
bills I and ferve as a fpecimen of the propi;!
method of calculating from them. It is in4
deed extremely to be vyiflicd, that they were
iefs imperfect: than they are, and cxtende4
further. More pariihes round London might
be taken into them; and, by an eafy im^
provement in the parifli regiftcrs now kept,
they might be exte^ideid tlirough all the pan

conHderably greater in New-England^ than that given by.
Dr, HalUfs X^ble, In 'New 7f'^> I ^^^^ f**^ ^^ num-,
ber of people under i6, wa^ found to be almoft equal iq
the number above 16. Suppofe, however, that in Netu*
England^ where the increafe is flower, the proportion I
have mentioned is only 16 to 20 ; and then the wi^ok.
number of people will be 720,000.

I cannot conclude this note without adding a remark ta
remove an objeilion whJch may occur to fome in reading^
Dr, Heberden's account of Madeir^^ to which I have re-
ferred. In that account 5945 is given as the number of.
children under feven in the ifland^ at the beginning of ther;
year 1767. The medium of annual births, for eight,
years, had been 2201 ; of butials 1293. In fix years^^
therefore^ 135206 muft have been born j and if, at tljc
end. of fix years, no more than 5945 of thefe were alive^
1 210 rouft have died every year. That is 5 almoil alf
the buri^ in the ifland, for fix years, muft have bcea.
burials of children under feven years of age. This ii^.
plainly incredible^ and, therefore, it feems certain, that
the number of children under feven years of age muft,.*
through fome miftake, be given, in that account, 30CO
or 4000 too little.

7 tiikQft

the Sfati of %onAoxk, PopuiMt^fi, kc. 3tt

fiiibes and towna in the ki^^dcun* The ad«
vantages arifing from hence would {)e veryr
coniiderable. It would give the precife hw
according to which humaa life wades in its
different ilages ; and thus fupply the neceffary
Jata for computing accurately the values of
all life- annuities and re^uerfi^n^i. It would^
like wife, (hew the different degrees of health-*
fulnefs of different fituations> mark the pro^
grcfs of population from year to year> keep
always in view the number of people in the
kingdom, and> in many other refpeds, fur-^
nifh inflruction of the greateft importance to"
the flate* Mr. De Moivre^ at the end of his
book on the Doiftrine of Chances, has re-
commended a general regulation of this kind ;
and obferved, particularly, that at leafl it is
to be wifhedy that an account was taken, at
proper intervals, of all the living in the king-
dom, with their ages and occupations i
which would, in fpme dpgree, anfwer moft
of the purpofes I have mentioned.— -But,
dear Sir, I am fenfible it is high time to
finifli thefe remarks* I have been carried in
them far beyond the limits I at firfl in-
tended« I always think with pleafure and
gratitude of your friendfhip. The world
owes to •you many important difcoveries)
and your name muft live as long as thefe
is any knowledge of philofophy among man-
kind. That you may ever enjoy all that

? 2 can

212 On tifi ExpeSfatlon i>f Lives ;

can make yoa mofl happy^ is the fincere
wifli of.

Sir,

Vour much obliged.

and very humble Servant,

< '

Ncwineton-^.rccn,
April 3, 1769.

Richard Price.

% •

POST-

the State of London, Popuhtrion^ &c. 1 1 1

POSTSCRIPT.

AT Edinburgh^ biHs of mortality, of the
fame kind with thofe in' London, have
been kept for many ^year's. ' f have, fincc
the foregoing letter Was written, examined
thefe' bills, and formed a Table of Ofeferva-
tions from them, as I found them for a period
tf 20 years; beginning in 1 739, and ending in
1758. — As this is a town of moderate bulk,
and feems to have a particular advantage of
fittiation ; I expecflcd to find the probabili-
ties lof life in it, nearly the fame with thofe
at BriJlaWf Northampton and Norwich ; but I
have been furprized to obferve, that this is
northe cafe. During the period I have men-
tioned, only one in 42 of all who died at
EidinSUrgh, reached 80 years of age ; which is
a fmaller proportion than attains to the fame
zgc in London. See p. 203.— In general; it
appears,, that the probabilities of life in this
town are much the famte, thro' all the ftages
of- life, with thofe in London, the chief diffe-
rence being, that after 30, they are rather
lowtr at Edinburgh. — It is not difficult to ac-
count for this. It affords, I think, a link-
ing proof of the pernicious effedls arifing
from uncleanlinefs, and crouding together
on one fpot too many inhabitants. At
Edinhurghy Mr. Maitland fays, ** the build-
<* ings, elfcwhere called bgufes^ are dehomi-

P 3 ^ ** nated

S 1 4 Dn tie Expe&atiM of Lhes i

natcd landii and the apartments /m other
places n^mtd^Jiprie^^ herp called boufes^ arc
*^ lo many freeholds inhabited by different
**^ families i whereby the houies are fO' eic*
^' ceflively croudpd with people, that 4mi
** inhabitants of this city may be juftly v^
^^ fumed to be more nun^cfous than thoie c^
** fome towns of triple its dimeofions/* ScQ
^aitland^s Uijiory (^ Edinburgh ^ p. I4Q, i
Xn the year 17481 the whole number t&
apartments ox families \xv the city and lihtftiei
9f Edinbut%h9 was 9064. .This Mr. idT^^^x
land mention^ ^ the^i^lt of partiGular t,%v^
minatioHy an4 undoubtedly rjght. lb. p. 217^
fi8,-»^In 1743^ an acc^uTdtte account lyat
taken, by the d^fire c^ this writer^ of thd
22umber oi families and inhahitiintf in the ]>a*«
rifli of St, Cutbbert. lb. p, 1 7 1 - The^ atimheo
pifymilies was 2.3.70, ^nd of inhabitants at all
ages, 9731. The proportipB, therefore, of
inhabitants to families^ wa$ 43V to r ; asd^
fuppofing this the truo projJprtion ^for cfaa
whole town^ the number of: inhabitants wiii
be 47V multiplied by 9064, qn 37,i.6a4**<»
The yearly medium of deati^ in the tawn
and liberties for eight yearsj from 1741^10

J74^> V^^ *7^3» -'^^ ?• ^*^ ^^^ ^^^* Andi
confeq^uen^ly, e?is^ in 2o4"die^aaBually;.

Mr« Ji^/Vi:!^^, tho' pq^fled of the data.

from which thele conclufioas neceifarily foi<«>*

lowed^ has m^ade the number of inhabatantl

50|i?Oj i^ ^9P^^^u^c$ of a difpofition: ttf

the State ^London, Population^ &c. 215

cxft^tfatc in t^^dfe fnaftcrs, and of sffuming,
WieBdiit any rikfoh, a 48tk ntrt of the inha-
IMtanis as dyi^^ klintialiy;
* In page 220, lie txbrcfles much furprize
in ftidtrtgi that ttie rnirtiber of males in this
rtWii'Wfe lefs than'the haihber of females,
ki fli^ |>ropdrri6h of ;J to 4; But this is by
kil'rtfc^s peculiar to Edinburgh.
- -All i have bWn fiyihg muft fee underftood
of tfee ftate off Erhnhurgbi \ before the year
l^j^S. The bilk, for the Mft 12 years, have
been to irregular, and fo different from the
iktiat bills for the preceding years, and from
$H tWtber bills, that I rannot give them any
crqrfit. Either fome particular incorredlnefs
has crept into the method of keeping them ;
if there has been feme change in the ftate
of the town which renders them of no ufc.
Prt^bably the former is the truth,

■

Frohi the note m p. 206, it appears, that
fee chrfftcnings and burials at Paris, come
very ntear to equality. This once led me to
fiifpedlr, that there muft be fome particular
finguianty in the ftate of Farisy which ren-
dered it much lefs prejudicial to health .and
popcilation than great towns commonly are.
Biit better information has lately obliged me
fo entertain very different fentimcnts.— The
difference between the births and burials at
FartSy f* niuch greater than the bills ftew.
*^ Children here are baptized the inflant

P 4 " they

€€
H

a 1 6 On tiff Expiration tff Lives ;

'' they are boon ; andu in a day or two af*
** j^fwards. it is the cuftom to fend them to
the adjacent viiiageb tl? b^ nurfed, A
great number, therefore, of the intanib upra
at Paris die in the. country^ and tbefe
appear only in the regifter of chriften*
^' ings." See a book entitled the Fdice
of France y page 127. .And Buffon's Natural
Hiftory, Tom. IL at the eod. — " All the
children alfo received into the Faundlmg^.
Ho/pital, arc ioimedj^tcly.fent to be surf-
ed in the country, at a diftance from Parisi
whjere they remain 5 or 6 years ; at tl^e end
of which time they are, brought again to
Paris, fhe boys to be placed in the fuburbs
of St. Antoinef and the girls at Salfetriere^
^' to he'furtiier maintained. 'till th^y aiu;ive at
*' the age of twelve years. '^ Police^ of Fr^mcep
p. 81. — The following -paflage in the fame
writer, containing a further account of this
Hofpital, is important^ and- therefore, tho'
long, I cannot help; tranfcribing it.— *^ Let
•* us.fuppofe, that out of 4000 childrep; an-
nually carried into the country, two^thirils
may die, during the iive years t^ey are
*' deilined to remain at nurfe ; io thj^t only
1333 would con^^antly be the annual
number fent back to Paris ; who,, being,
kept at the two Hofpitals St. Antoinf and
Salpetriere ]m^ mentioned, 'till they are.i.a,
and fucceeded by a like iiumber each year,
the total number compoiea of all brought

''in

€€
€€
€t

€t

4€

€€
€€

€€

the Stati of hon&on^ Papulation^ &c. i\j

y in fbe-fuCceffivc ycar$, would make the
f conftant refting (lock to amount to 9331-
*• But ^ thcfe we will iuppoie a 5th part
?* to iJie every year. Yet cvctt. then the
^Vconftant refting ftqck of children ought to
*'. be 7465. How greatly then mtift we be
^^ furpijiiscd to fend, by the authentic account
**.takcfi_from tfeeir own. books^ only. 640
«« boys in the college of St. AntoinCf and not
f* il^ore thart 600* girls at the S'aJpetriere ;
*'* fo that 'the refting ftock of returned found-
^' ling^ appears to be.no more than 1240,
*• which being dedui^edfrom 7465, Nyill make
** the diiTerence in the deficiencies 622c,
*^ ^hat then becomes of. thcfe ?-rvAre they
'• 'reclaimed by their . parents ?— •Or do they
** perifti for fWant of care?— In anfwer to

which queftions^ it. was explained to me ;

that as many of th^ lower clais of people
** .were induced to tnarry, in order, to be ex-

V cufed from ferving in the militia^ £0 when
** thefe have children, which they are un-
** able to maintain, they ufually fei^ them to
** .this hofpital ; which, therefore, muft be

V lool^ed upon, as not only a charity for the
'^ care of expofed and deferted children whofc

parents are unknown, but alfo as a public
nurfiry for the fufteaance of the children
of poor people, who, tho' regiftered at the
** oiHce,1a]re often reclaimed from their coun-
•* try nurfes by t|ieir parents. This accounts
^* in fome meafure, for the fmall ftock of

*♦ children

<<
<(

€1

a 1 8 On the Expe^tkn ^ Lives j

•* thildwn broijght b«:k to the h6lj)i«li ai
i' pi?ri>-— The further difference is ful|)feaa4
f* to te owing to thfc iftfumcient HotfHftitrierit
" thcjTJJeceive J as this pafticular choHty, as
** well as the General Hofpital, idoptsAat
** piwpbfterotts method of iakin^ in an tm-*'
^' limised* number, while thfeffe is bhly i IJ-
^« mited income for their fabfiftence." \Wi
|>age 8^« ■ • .• .. •

Thefe fa£ts pr^ve, that; at the !feifte tftnc
that the regiftef of cbrijienings at Paris touff
be fuil, thfe regifter of Awh^^ muft be ?cry
defideftt, .Let thfe defietencies be reckoned
at 37^0 ; - and, coni<3qe*ntly, -tht ' aSiMiaf
buriuls at 43,100. The ia&ttaal k^ht^^jot
weiidingS; given in p, 206, is 4400 ; iftd,'
therefore^ tdbe number of perlbns whoTh^ry
annuafHy mmft be 88o<S, • Eteduift a ©th piart (^jf
for iffidoti^s^nd wido'wers, and 7134 ^^'ill-bH
riie iwmbdl' of virgihs aiid batcheiors m^rf^ying
amiu^ny.'i-^The diff^rtnce between the Ithrii?
tcningte atid burials' is 4060 5 which, there-
fore, is the number of ab^tual recruits from
the (Country. Thefe, in general, thuft -be*
^erfon j in mature life. Sii^pofe 3060 of thech*
to mafry after fettling at Paris. Then^ ^ 1-34
levelled by 3000, or 4134 will be the nufai-
feer of perfons borii a* Pa^is who grow up to*
Aiarryi' and r4,966, at near four-fifths of alT
who afe bbrn at Paris^ "v*iil be the num^eK
dyirtg annually iri childboddand celibacy:

' U) Vid. Note,' {f. Y55,

The

the StaU ^London > Population y hoc. i r ^

Tlie' ftppdflltons <yn which I have made
this computation fcem moderate ; bat if any
one thinks otherwife, he may make the fame
calculation on any other l!bppofitions.

The births at Paris are above four time9
the weddings ; tnd it may feem, therefore^
that here, its weH as in the moft healthy
Country lituations, every wedding produces
above four chiklreD. I have obferved no-
thing like this in any other great town.
Many children born in the country are, I
fiippafe (^)» brought to the FoundKng-Hof-
pttaly and there chriftened. This Hofpital
fiiay Hkewife occalion ^ more than common
^Apiber of illegitimate births. And» bcfides^
fdme who leave the country to fettle at Paris^
Ittay come thither already married. Tbele
are circumftances that will fwell the regifter
of births, withoat having any effeft on the
weddings. I da not, however, know that
• jtny of them take place at Paris i and, per-*
Jbaps, it muft be granted, thatMt is diftin*
guiifaed in this refpeft frt)m moft dfher towns/
Nor can I wonder at this, if it be indeed
truc,;)ot only, that all married men in France'
are excufed ferving in the militia from whence
draughts are made for the army,^ but alfo,

{it) *^ If the parents of a child brought to this Hbfpita!
<^. are known, the regificr of its baptifm muft be pro-
«^ duced. Jf cho parents are unknown, the child muflr
♦* be bapdfed after Being received," Polm of France

that

220 On the Exp^Sfatim of Lives i

that ^ fifth of all the children born at Vdrh
arc fent to the Foundling- Hofpital {a)^ Thcfe

m I

•

{a) Sec the ;Polide of France, p. 83. — This writa:
adds,,that'a third of all that die at Parii die in Hofpitals.
« In Kht Hctil DUu (a great Hofpital, fituated in the
** middle of the city) we may, hr fays, behold a horrid
^* feene of mifcry \ for,,. the beds being too few for the
<< numbers admitted, it is common to fee 4, or 69. or
** even 8 in a bed togetRer, lying 4 at one end, and 4
<< at the other, ill of various diAempers in feveral de-
^^ gree$;.fome bad^ others worfe; ibnr^ dyii^, others
«* dead.— Above a ffth of all admitted to this. Hofnitd
♦* die ; the annual numbers admitted being 2*1, ?2^ The
«* mediam of deaths for three yeaA from 175'! to 1753*
** 4650. — The medium of deaths for the fime.yeanmi^
•* tf//the Hofpitals was 6.i8i-'' Ilf* P- 85.-^Iii 0ur,two
great city Hofpitals, St. Thomas's and St, Barthokpitw^^^
iboxxt 600 die annually ; or one in 13 of all adniitte<I as
]n-patitnta.^r^^— An account of. the Hotel t>iiU at fd»is^
Qiuch the fame with that now given, npay be fouadm
the Memoir's of the Tear Two Thoufand Five Hundred lately
publlfiied, and tranflated from the French by ff^. Hoopefi
M, D. ;** A dtizen or ftranger * (this write^^fays) whb
fajis (icjc, j&nd is fent thither^ is imprifoned in a noifo«i9
bed, between a corpfe and a perfon expiring, in agonies,.
** to breathe the noxious vapours from the dead and the
^^ dying, and convert a fimple t^ndi(pofitton-into a cruel
*' difeafe. — ^ix thoufand. wretches are.crouded togct^ci^
** into this Hofpiul, whei:e the. air has no free <;irculaA
** tion ; and the arm of the river which flows by,* re-
^* ccives all its filth, and is drank, aboundirig with the
V feeds of corrwption, by half the :city.^' The lArukti
Hofpitals, it appears, have gteatly the advantage \ but,
indeed, with refpecl to Hofpitals in general,' as new com-
Jiru£led and regulated^ I cannot help fearing that they
caufe more difiempers than they cure, and deflfroy tnore
lives than they fave. See Tbaugbis on Nofpitaisy by Mr.
u^/if/a,'fHrgeQn, together with a Letter to the Author,
by Dr. PercivaL ■ , '

arc

tbt Suit£ of hondb^m^ Papulation ft^c. 221

are encouragements to marriage that no other
city enjoys. It has been feen that the Found--
ting^HoJptaU tho' attended with this effedt,
is, probably, in the higheft degree^ pernici--
ens; but it is to be wifhed, that foitie policy
of the iame kind with that Jirft mentioned^
was purfued in this kingdom.-— At the end
of the 2d vol. of MonfieurD^B»^»V Natural
Hiftory^ there are Tables formed from the
Obfervations of M. Du Pre it S. Maur^ of
the French Academy ^ containing an account of
the ages at which 1 3, 1 89 perfons died in three
parifhes 2XPari5\ and alfo, of the ages at which
1 0,805 perfons di^d in ! 2 country parifhes and^
villages near P^m.— According to thcfe Ta-^'
bles, many more die in the beginning of life,
and muchy^^r in the latter part of life, in'
the country than in Paris. But the circum-
ftances of Paris^ and the country round it,
are fuch, that no argument can be drawn
from hence in favour oi Paris. Many of the
children dying in the country, are children
ient thither from Paris to be nurfed ; and,
on the other hand, manyf perhaps mo/ij of
thofe who die in old age at Paris, are per*
fons who have removed thither from the
country, ibme to Ho/pifals, and fome to
places and fettlements. It is evident, there-
fore, that thefe Tables give a reprefcntation ,
of the probabilities of life at Paris, which,
when compared with thofe in the adjacent

^ country.

0« tU M:fC]^^Hfiiim (f Xivai

CQoqtry (4), is juft.tfae r^wffc of the trutJl)
Were the ehildren born at Pans^ who dio
in the country, to be transferred to the town
regifter; and, on the cdotraryt the adulta
bom in. the country, who die at Paris^^ to
be tran«fcfred to the country regiftcc, there
1$ aoreafan to doubt, bat that the profaa-
bilitiea of life at Paris^ would be found z%
low^ in cbmptLrifon with thofe in the coun-*-
try,, a$ the probabilictes . of life it\ London
are; or, perhaps, much lower.— Thi^ ob-
jfervation is applicable, in fome degree, to
moil other great towna^ and,, inr genera^
c(n account of the migratiom from the-coun*
try to towQus, navies and- armies, we* may be
l^tisfied, that we err oa the fide of defeSt^
whenever we j udge of the probabilities of
life in the country f, from the numbers dy-
ing in.iche feveral ibgts.of.life; and^ on the
fide ^i^excefi^ whenever^ i^ the fanaie way, we
judge of the pjobabilitiea of life in toigns.
And this> it is obviou^^ hacs a tendency to
con&'ni all that has been £aid in the prcccd-^
iog £0ay^ concerning the pernicious etfedla
of gceat tQwns on human life.

There are Several ordonnances and arrets of
which iuc the .boundaries; of Ptnisp

(0}^ It is for x\i\$ reaibn (ha« thefe T^bles^ w}>t|) com*
bined) exhibit judly the rncdn probabilities of life for town
ahdcountr/ taken together; ^i\i that the TaMe of the
dicremenu oi lifs deduced* from eh«m- by M. Buffm and*
Uli, Qu Frff agrees nearly with Dr. HalU/s Table.

and

*

the State afLoskdon, Population^ k^c. 22%

iad prohibk all new buildings beyonfl thofp
boundaries .—The reaibns of this regul$itioa»
a; fct forth in oije of thefe arrets^ apc tqt*
markable ; and it will not be improp^er to
recite them.—" By the exceHive aggrapdia*
*^ ing of th^ city^ it is faid^ the air woulfl be
'^ rendered unwholefom^, and the cleaning
•* the ftreets more difticult." — *' Augment-
ing the number of inhabitants would aug-
ment the price of provifions^ labour, and
**. manufadures/'-— ** That ground would be
'^ covered with buildings whi(:h ought to b^
** cultivated in raifing the neceflary fubfift*
" ence for the inhabitants ; and thereby ha-
** zard a fcarcity.*'— " The people in the
*^ neighbouring towns and villages would b^
'^ tempted to come and Ax their refidenc^ in
" the capital, ancj defcrt the country."-^*n
" And laltly ; the difficulty of governing fo
** great a number of people, would occafion
•* a diforder in the JPo/ice, and give an oppor-
•* tunity to fogues to commit robberies and'
% murders (a)/'

No one can think overgrown cities greater
evils than I do. But, yet, I can by no means
approve of this, policy. The eiFe<3; of it moii
be^ crouding together too many peof4e with-
in the prcfcribed hoandaries, and rendering
a town more the feat of uncleanlinefs* infec-^
tion and di£eafe.— nThe number of haufes in

(a) Vid» Police of France, p. 130.

Paris

fift4 *^* ^^ Expe^attan of Lives ^

Paris is reckoned about 28,000 (^), but the
number of inhabitants, ffuppofing a 20th
part to die Annually, and the true number of
burials to be 23,000) muft be 460,000 ; or
aibout 16 times the number of houfcs.

It is happy for* London, that there have
been no laws to reftrain its increafe. In con-
fequence of being allowed to extend itfelf on
all fides into the country, the inhabitants
now take near twice the room to live upon
that they did ; and it is become lefs the means
of fhortening human life. See p. 191, 192,

and 204.

«

In page 206, I have given the annual me^
dium of births, weddings and burials at Ber-
lin, from 1755 to 1759. — In 1747, an ac-
count was taken with the utmoft care, by
the order of the King of Prussia, of the

la) Vid. Police of France, p, 130.

1 find, in a Book entitled, Reckerches fttr la Popula^
iion des Generalites d^Auvergne, de Lyan^ de Roucn^ '&c*
by M. Messance, and printed zi Paris in 1766, tiK
number of houfes at Paris is given 23,565, from a ca-
pitation tax in 1755 y and the number of families 71,114.
There muft, I fuppofe, be fome deficlenc^ies in this ac-
count; but M. MeJJance^ by allpwing moft extravagantly
(See Note, p. 183.) 8 to a family, infers from it that the
number of inhabitants at Paris is 568,912. — On very
unfatisfaflory grounds alfo he makes the inhabitants of
France to be near 24 millions. Sufmilch calls them 16
millions <; and Marjhal Saxe^ in his Memoirs on the Art
of War, after obferving that VaubarCs calculation had
made them 20 millions ; adds, that their number at the
time he wrote was far inferior to this.

7 number

the Siate ^Lohcton, Population, Uc. iif

ftumber of inhabitants in this town ; and, it
Was found to be i07»2244--^In order to be
more certain, ay^c^;?^ account was taken th^
fame year i and the numbef foUnd the fame
within 2oo.-^In 1755^ the inhabitants were
increafed to 126^6614 Their number^ there-
fore, in 1758, could fcarcely be lefs than
134,0001 and muft have been to the annual
burials nearly as 267 to i •— <^This proportion
is higher than could be expedted in a town
£0 confiderablei and alfo fo much croud^
cd, as to have^ at an average, 16 inhabit*
tants in every houfe. But an obfervation
already made, muft be here remembered ^
*— Berlin, for m^ny 3rears, had been in-
creating very faft, by a conflux of people
from the furrounding country and provinces*
About the year 1700, the medium of annual
burials was no more than looO. In 50 years^
therefore, it has more than quadrupled it-
felf.*— In a city increafing with fuch rapidity^
the ratio of inhabitants to the annual deaths,
muft be greatly above the juft ftandard.— ^
Were there now, fuch acceilions to London
of deferters from the country, in the begins
ning of mature life^ as would caufe the
number of inhabitants to increafe at the rate
of 10,000 every year, it would in 60 years
be doubled ; and the proportion of inhabi-
tants to deaths would rife gradually, 'till it
came to be about one- third greater. Berlin^
we have ieen^ has, in fad, increafed Elmore

Q^ than

226 On the ExpeSiation of Lives ^ &c.

than double this rate ; and, therefore, the
number of inhabitants dying annually in it
is in reality very high.

The ingenious Sufmilcby to whofe works,
I owe my information concerning Berlin,
makes the proportion of people who die an-
nually in great towns, to be from V^ to Vt ;
in moderate towns, from Vt to tV ; and in the
country from ttt to 7'^* — The obfervations
and fadls in this Eifay, joined to thofe which
will be found in the 4th EiTay and the Sup-
plement ^ prove, I think, that thefe propor-*
tions may be more truly ftated as follows.-**
Great towns, from xV or -^i-^ to tt or V^.
Moderate towns, from Vt to tV* The coun^
trjf^ from tV or Vv, to tV or Vr.— This, how-
ever, mud be underflood with exceptions.
There may be moderate to^v^ns fo ill fituated^
or whofe inhabitants may be fo crouded to-
gether, as to render the proportion of deaths
in them greater than in the largeft towns :
And, of this, Edinburgh, if it is not now,
was 20 years ago an example.— ^Thcre may
be alfo great towns in which, from a fud-
den increafe, this proportion may be le^
than in fmall towns : And of this I have juft
given an example in B£Rlin.

ESSAY

[ 227 ]

ESSAY 11.

On Mr. De Moivre*s Rt^Ies for caU
culating the Values of Joint Lives.

TH E calculation of the values o{ Jingle
and joint lives, from given Tables of
Obfervation, being tedious and troublefome ;
Mr. De Moivre has had recourfe to two Hy*
pothefes^ which give cafy rules for this pur-
pofe ; and which, he thought, correfponded
with fufficient exadnefs to Obfervations.*—
The firft of thcfe Hypothefes is, that the pro-
babilities of life decreafe, as we advance from
childhood to old age, in an arithmetical pro-*
greffion ; or in fuch a manner, that the diffe'^
rence is always the fame, between the num-
ber of perfons living at the beginning of any
one year, and the number living at the be-
ginning of the next following year.— The
other Hypotbejis is, that the probabilities of
life decreafe in a geometrical progreffion ; or
in fuch a manner, that the proportioyt is al-
ways the fame, between the number of per-
fons living at the beginning of any one year,
and the number living at the beginning of
the next following yfear. — All the Tables
of Obfervation fbew, that the real law, ac-
cording to which human life waftcs^ comes

0^2 much

ii 2 8 Of the Method of calculating

much nearer to the former Hypothefis^ thar>
the latter. — In Tables III, IV, and V, in the
Appendix^ it is fo near the former HypotbefiSf
that the difference is fcarcely worth regard-
ing. According to this Hypotbefs^ therefore,
(accommodated to the Brejlaw Table, in the
manner mentioned in the note, page 2.)
Mr. De Moivre calculated the values oi Jingle
lives i and the rules founded upon it for this
purpofe are fo eafy, that an operation which
would otherwife take up much time, may
be performed almoft immediately.

By proceeding on the fame principles, the
values of joint lives might have been calcu-
lated ; but the rules for this purpofe derived
from thefe principles, are far from being
equally eafy in pradlice. Here, therefore,
Mr. jD^ Afo/Vr^ quitted hisfrfi Hypothefis;
and finding, that the fecond Hypothefis af-
forded, in the, cafe oi joint lives, rules that
were as eafy, as the rules given by the other
Hypothefis were in the cafe of Jingle lives,
he chofe to adopt this Hypothefis -, believing
at the fame time, that the values of joint lives,
obtained by rules derived from it, would
not deviate much from the truth. But in
this he was greatly miflaken. The values
of two joint lives obtained by thefe rules are
fo wrong, that in finding the prefent value, in
^fingle payment^ of one life after another, they
generally give refults which. are ryt^r^ garter
of the true yalue top great ; and about tnoo^

fifths

the Values ofyoint Lives. 229

^tbs too great, when the vahie is fought in
annual payments during the joint lives.—
Thcfe arc errors fo conliderable, that L think,
it of particular importance that the public
fhould be informed of them, in order to pre-
vent the inconveniencies and perplexities
they may occafion.

Mr. Simpfon fin the Appendix to his Trca-
tifc on the DoBrifie of Annuities and Rever^
Jions) hasobferved, that Mr. DeMoivre*s rules
fw finding the values of joint lives are wrong.
But I don't know, that it has been ever at-
tended to, that they arc fo wrong as I have
found them. Mr. Simeons remarks point
out chiefly the errors in thefe rules, when the
values of three or mtfre joint lives are calcu-
lated by them ; but, 'till I was forced to a
particular examination of this fubjeA by
fbme difficulties into which I found myfelf
brought by following Mr. De Moivre too
implicitly, I did not at all fufped, that any
fuch errors as I have mentioned, could arife
from thefe rules, when the values of only two
joint lives are calculated by them. Mr. De
Moivre, in confequence of other remarks
contained in Mr. Simpfin*% Appendidc^ altered^
in the 4th edition of his Treatife, fome of his
rules. It is furprizing he did not fee reafon
at the fame time to alter thefe.

That there may be no doubt about the
truth of thefe obfcrvations, I will juft men-
tion a few examples of the difference between

I

J 3 o Of the Method of calculating

the values of a given reverfionary annuity^
according to the rul6$ to which I have ob-
jedted, and the trtie values^ according to the
exadl method of deducing them from Mr.
IX? Moivre' s frft bypotbefis.

Let the propofed ani)iaity be 30/^ to be
enjoyed for what (hall happen to. remain of
the life o( a perlon now '40 ye^rs of age, af-
ter the life of another peiTpn of the Ame age;
The. value of the joint Jives (inCereft being
at 4 p0r cent.) is, by prphliem 2d of Mr,. Di
Moivre\ Trcatift on .JLifc- Annuities, 8.964$
which fubtra<aed from. 13.196, (the value
by Tabl^ VI, of a fingle-lMfe at 40) gives
4.»23:j which remaHi^<^n,.vflluUi plied by 30>
gives /. 126.9, or the v^^Iue of the reveriion
in a fingle prefent payment, Aod. 116,9,
divided by the foregoing value of the joint
liv^^i isy,i;44i}6 j of,/the value of the rcver^
iion < Ja anxiqal payments 4uring 'the joint
lives.— rBtrt xhe . true yajy^s .a^c v'. x 6%.i in a
Jingle, )3ayjii.«fnt, by Quell:, I; chap. L ; and
L r.o.'3> in annual payments, by Queft;iV*--r
The former values, therefore, are a quar^^
tir of. thse true, value too great. in^he^»-
^Zf pdyn%«ntj and ne^r tivo-f/ihs too great
in the auMai paym)ent$» . .

The tru0 value of the fame annuity, itxr a
life at 66, after anothexHfe of the -fame age,
is, (reckoning intereft tA before, at 4/tfr cAit.)
68/, in z. Jingle payment; and 13.5 in an^^
nual payments.-^But thefe values, acQording

to

tbe Values of^oint Lityes. 231

to the Problem juft qiloted, are 9 1 /. and 2 1 /;
one of which is near a thirds and the other
^bove balfikxc true value too great.

In unequal lives thefe errors may be no lefs
confidcrable.-»-*Thus 5 if tbe value of the pro-
pofed annuity, be required for a life at 70,
after a life at 30 years of age -, it wiU^ by
the fame Problem, be I. 26.5, in ^Jingle pay-
mi^nit ; and /- 5.I9 in annual payments during
the joint lives. £ut the tr^e values are 1 7 /•
and L 3*05.

- . Where 3 or more lives are concerned the
errors will be ftill greater,
. The true values of the joint lives, meif-
Ittpned in thefe Examples, have been calcu-
lated by a rule in page 16, of Mr. Simp/on s
Treatife on the Dodrine of Annuities and
Reverfionsj and explained in note (M) jip^
fendix. — To fave, however, a great deal of
trojible hereafter, I have thought proper to
calculate Table VII, which gives the exa<ft
values according to Mr. T>e Moivres Jirji
hypothefis, of two joint lives, for every five
years of human life, from 10 to 70.

This hypothejisy I have obferved, does not
diflfer much from the Tables of Obfervation
in xhcAppendiXy iorBreJlaw, Northampton and
Norwich. Between the ages of 30 and 40,
it gives the values oi Jingle lives almoft the
fame with the Brejlaw Table. Under 30, it
gives them fomewhat lefs ; and above 40,
fomewhat greater. But it ought to be re-

0^4 mem-

« 3 * Of the Method of calculating^ &c,

xnembcrod^ that wherever it does this^ it
gives, at the fame ages, the. values of the
joint lives alfo too little or too great i and thatj^
confequently, the refults from it|^ in calcula-
ting the Values of Reverfionsj and of the longejt
of given lives, come fq much nearer to exf
adn^is.

The rules to which I have objeded are tho
only ones given by Mr, De Moivre^ in all the
editions of his Treatife on Life-Appuities^
But it {t,txti%y this great mathematician be-
came at lafl: fenfible, that they were too in->
correct ; and, therefore, at the end of the laft
edition of his Treatifc on the DoQrine of
Chances^ page 320, (a work which gets into
comparatively few hands) he has given other
rules which come nearer the truths But
even thefe rules produce errors io great in
many cafes, (particularly when combined
with the errors of the hypothefis) that U
wili^be bcft never to uib then}*

ESSAY

[ 233 ]

ESSAY III.

Of the Method of calculating the
Values of Reverjions depending on

SurvivorJI^ip,

ALL Queftions relating to the values of
lives and Teveriions» are at prefent of
particular importance in thiskingdom. Much
bufinefs is continually tranfadted m this way s
and any considerable errors in the methods
of iblving fuch queitions, muft in time pro*
dace very bad confequences.^^The deiign of
the following obfervatioos is to point out a
particular error, into which, there is d^ger
of fallingt in finding the values of fuch re*
verlions as depend on furvivor(hips. In do-^
ing this, I fhalU in order to be as plain as
poffible, take the following cafe. ^' A, aged
40, expedts to come to the poflefiion of
an eftate, fhould he furvive B, aged like*
^' wife 40. In thefe circumftances he offers,
*^ in order to raif^ a prefent fum, to give fe-
^' curity for 40 /. per annum^ out of the eftate
^^ at his death, provided he (hould get into
7 ^* poiTcfs-

€€
€€

234 Of the Values o/Reverfions

** poffcflion ', that is, provided he (hould fur-
** vive B. What is the fum that ought now
** to be advanced to him, in confideration of
" fuch fe^fcrity, recfcbniqg compound inte-
** reft at 4 per cent. ?"

Mr. De Mohre's diredions in his Trea-
tife on Annuities, Problems 17th and 20th,
lead us to^feek' the required fum in this caic>
by the follawing procefs.

Find firft> the prefent fum A flioiild* re-
ceive, for the reverfion of 40 /. per arinum for
ever after his death ; fuppofing it not depen-
dent on his furviving B. The prefent value of
fuch a rcwtfion is ** !dhe?(ir)rvalue of the fife
*^ fubtffi^cd from th£\pfrf£tmty, and the riir-
** -mainder multiplied by the afinualMfentL'^^?^
The vahac of the life is, by Table VIj iijii 96.
This fujbtra<fted fpom!25^ ^btfer^etuity^ leaves
1 1.80 j:whieh, multiplied by 40, givcs7.i472;
the value of the fuppoied eftate,, af tor Jthc life
of A. > B«Ait,cas Mr. Hz Motnyre obferved, tiie
tender havuig a chance lx> lofe his moaey, a
compenfatioa ought to be made to him for
the rifk h^e runs, which is founded on the
poiBbilityi, ttrat ajmaatif 40 years of ^e may
not furvive another povfon of th^ fame age.
This chance IS an rj«<s/ chance ; and, there-
fore, halfithe preceding fam,- or 236/. is the
money which (hould ) be. advanced; nbiv. on
the expectation. mentioned.

{a) By Schoiium, p. 34, and Problem 26th, p. 293,
©f Mr, Simffiriz Sclc<a Excrcifcs.

This

€€
€€
€4
€€

depending' on Surthorjhips. 235

* This folution carries a plaufible appear-
ance; and naoft perfons wilU probably, be
ready to pronounce it right ; nor will this
be at all wonderful, as fo great a mailer of
the£e fubjc<3s as Mr. De Moivre appears to
have been mifled by it. — ^Nothing more isr
neceifary to prove it to be fallacious, than
proceeding in the fame way to foive the §61^
lowing (imilar Qucftion.

A, aged 40, offers to give fecurity fof

40 /. per annum, to be entered upon at his

death, provi(ied it fliould'happeh iefore the

death :of B, aged likewiie 40. What fum

*' ihould now be advanebd : to him for fuch

*'^ a rever£on, intereft beiog reckoned at 4

" per cent. V'

.In folving thpg Problem, agreeably to the
method juft (icrcribed, wc/are to find the va«
lue of 40 /. per annum ^ to • be entered upon
vertainly at the death of A' ; and then to muU
tiply this value by the chance that A ihall
not furvive B, or by i; and in this way th?5
anfwer comes out the fame with that already
given*

Now it. may be eaiilyfeen, that this muft
be wrong. The value of a reverfion, to be
received when, a peribn of a given age dies,
cannot . be the fame, whether the condition
of obtaining it is, that he {hall die before, or
that he (hall die after another perfon. That
is, whether it is provided, that a purchaferi if
he fucceeds, (hall get into ^o^t^ow fooner or

7 later.

4€

* 3 6 Of the Values of Reverjionf '

hter. The reverfion in the latter cafe mu'ft^
without doubts be of lefs value than in the

former.

«

The firft Queftion here propofed, refolves
itfdf into the following general Queftion.
" What is the prefent value of a given re-
verfionary eftate^ to be entered upon after
the failure of two lives, provided one in
particular of them (hould be the longeji

life r

Now, the prefent value of an eftate to be
enjoyed for ever, after the failure of the /m^-
e/f df two lives, is " the value of the longeji
^* of the two lives^ fubtra(fted from the per^
*' petuity ; and the remainder multiplied by
** the annual rent of the eftate/'-'-^The value
of the longeji of two lives is (as4l well known)
the value of the v^o joint lives, fubtra<fted from
ikn^Jiim of the (4) values of the two Jingle
lives. In the prefent cafe, therefore, it is
9.82, (the value of two joint lives at the age
of 40 by Table VII,) fubtraded from twice
1 3. 1 96 ; (the value of ^Jingle life at the fame
age by Table VI>) that is, i6,57 y^^i^'s pur-
chafe. And this fubtraded from 25^ (the
perpetuity) gives 8.43 ; which, multiplied by
40, gives /. 337.2, the value of the given eftate
were it certainly to be enjoyed, after the ex-

(tf) See Mr. De Moivrt on Annuities, Problem IV ;
or Mr. Simpfon^s Do^rim of Annuities and Rtvirficns^ Prop
Weaill. • ^

tindlion

depending on ^urvhorjhips. 237

tioAlon of the longeft of two lives both 40 ;
that is, whether one or other of them failed
lailr But that A's life in particular fhould
fail laft, rather than B's, is an even chance.
The true value of the reverfion, therefore,
is half the lail value, or /. 168.6.

In like manner. The fecond Queftion is the
fame with the Queftion, " What is the pre-
•* fent value of 40 /. perann. for ever, to be en-
•^ tered upon after the extindion of ivro joint
•* lives both 40 ; that is, whenever either of
'< them (hall fail i provided the firft that fails
** (hould happen to be A's life in particular?**
---*And the anfwer is found by fubtradting the
prefent value of the two joint lives from the
perpetuity f and multiplying the remainder by
t, or by the chance that A in particular
ihall die firft : And this will give the re-
quired vahie, /. 303.4 (^).

In (hort. It appears in both thefe cafes,
that, according to the firft method of folu*
tion, we are to fubtraft from the perpetuity
the value of one of the fingle lives i when, in
ih^ former cafe, the value of the longefi of the
two lives, and, in the latter cafe, the value
of th^xr joint continuance, ought, in reality, to
befubtradted. I need not fay what prodigi-
ous errors may often arife from hence ; and
how unfit fuch a method of folution is for
pradlice.

(a) I hare, tho' fcarcely neceflary, given a dcmonftra-
tion of thefe Solutions in the Appendiic, note (N).

Mr,

Mr. Simp/on^ in p- 322, of his Seledt E^f-
ercifeS) fpcaks on this fubjedl in the folio w«
ing manner.—** I have been very particiUar
on thefe kinds of Problems ; and the more
fo, as there has be^n no method before
publiflied, that 1 know of, by which they
can be rightly determined. 'Tis true, the
manner of proceeding, by firft finding the
probability of furvivorfiiip, (which me-
thod is ufed in my former work, and
which a celebrated author has largely infift-
ed on in three fucceflive editions) may be
applied to good advantage, when the given
ages are nearly equal; but then it is certain,
that this is not a genuine way of going to
work, and that the conclufions hence deriv-
ed are at beft but near approximations/'
This excellent mathematician has here ex*-
preffed hinifelf much too favourably of the
method of folution on which I h^ve remark-
ed. — In both the cafes I have fpecified, the
ages are equal i and yet, in one of them the
error is a good deal above a third of the true
value, and in the other a Jiftb : And, it is
obvious, that in cafes where three equal lives
are taken, the errors will be much greater.
— Mr. Simpfoti^ Obfervations in this palTage
are true only, when applied to a different me-
thod ufed by himfelf, in the 28 th and fol-
lowing Problems of his Treatife on the Doc-^
trine of Annuities and Reverfions. This me-
thod is exadt when the lives are equal i but,

it

depending on Survworjhips. 239

it gives refults which are too far from the
truth, when^ there is any confiderable inequa-
lity between the lives.

It is with reludance I have made fome of
thefe remarks* Mr. De M?/'z;r^ has made
very important improvements in this branch
of fcience; and the higheft refpedt is due to
his name and authority. This, however,
only renders thefe remarks more neceiiary.

In the firft Chapter (Queftions loth, i ith,
1 2th, 14th, &c.) I have given a minute ac*-
count of the method of finding, in all cafes,
the values of the reveriions which have been
the fubjedfc of this JBifay.

1 . I

ESSAY

( 24° 1

ESSAY IV.

I

4.

Obfervations on the proper Method of
cohJiruEiing Tables for detertnining
the Rate of human Mortality^ the
Number of Inhabitants^ and the
Values of Lives in any Town or
DiJiriEl^ from Bills of Mortality in
which aregiveny the Numbers dying
annually at all Ages.

IN every place that juft fuppotts itfdf ia
the number of its inhabitants, without
any recruits from other places ; or where,
for a courfe of years, there has been no in*
creafe or decreafe, the number of perfons
dying every year at any particular age, and
above it, muft be equal to the number of tha
living at that age.— -The number, for exam*
pie, dying every year, at all ages, from the
beginning to the utmofl extremity of life, mufl,
in fuch a fitu^tion, be juft equal to the whole
number born every year. And for the fame
reafon, the number dying every year at on^
year of age and upwards ; at two years of age
and upwards ; at t6ree and upwards, and fo
on ; mud be equal to the Qumbers that at**
tain to thofe ages every year; or^ which is

the

Of the Method of formings &c* 241

the fame^ to the numbers of the living at thofe
ages.' It is obvious, that unlefs this happens^
the number of inhabitants cannot remain the
fame. If the former number is greater than
the latter, the inhabitants muft decreafe ; if
Icfs, they muft mcrea/e.— From this obfcr-
vation it follows, that in a town or country
where there is no increafe or decreafe, bills
of mortality which give the ages at which
all die, will (hew the exa(% number of inha-
bitants $ and alio the exa<3 law, according to
which human life waftes in that town or
country.

In order to find the number of inhabitants ;
idle mean numbers dying annually, at every
particular ' age and upwards, muft be taken
as given by the bills, and placed under one
another in the order of the fecond column of
the 12th Table in the Appendix. Thefe
numbers will, it has appeared, be the numbers
of the living at i, 2, 3, &c. years of age ; and,
confequently, the fum, diminiftied by half
the number born annually (^), will be the

whole

(«) This fubtradton is neceflary for the following rea«
fon.— ^In a Table formed in the manner here direded, it
is fuppofed, that che numbers in the fecond column are
all living together at the beginning of every year. Thus ;
the number in the fecond column oppoftce to o in the
firft column, the Table fuppofes to be all jull born to-
gether on the firft day of the year* The number, like*
wife, oppofite to 1, it fuppofes to attain to one year of

R age

242t Of the Method offitming

whole number of inhabitants.— In fuch a To-
ries of numbers, the exce(s of ea(;h nuipibcr
above that which immediately follows it, will
be the number dying every year, out of the
particular number alive at the beginning of
the year ; and theie exceiies fet down regu<<-
larly as in the third column of the Table to
which I have referred, will (hew the diffe-
rent rates at which human life waftes thro'
all its different periods, and the different
probabilities of life at all particular ages.

It muft be remembered, that what ha<
been now iaid goes on the fuppofition, that
the place, whoie bills of mortality are given,
fupports itfelf, by procreation only, in th^
number of its inhabitants. In towns this very
feldom happens, on account x>f the luxury and
debauchery which generally prevail in them.
They are, therefore, comnoouly kept up by
a conftant acceflioii of ftrangers ovfetilersp

age iuft at the fame time that the former number is borik
And the like 13 true of every number in the fecond co-
lumn.— During the courfe of the year, as many will die at
all ages as were born at the beginning of the year ; and,
conie^ttcotly, there will be aa excefs of the number alive
«t the beginning of the year, above the number alive at
the end of the year» equal to the whole number of the
{annual births ; and the true number conftantly alive to*
gether, is the arithmetical mean between thei/£ two num-
bers ; or, agreeably to the rule I have given, xYktfum of
the numbers in the fecond column of the Table, IciTened
by half the number of annual birtbs. See £flay I, page
J 74.

who

Taites tf OykroAtioHs^ Uti x^)

who remove to them from country parishes
imd villages* In thefe circumftarifcesi in or«
der to find the true number of inhabitants^
and probabilities of life, from bills of morta-
lity containing an account of the ages at
which alt die i it is necelTary that the pro-
portion of the annual births to the annual
fettliers (hould be known ; and ttfo the period
of life at which the latter remove* — Both
thefe particulars may be difcovered in thd
following method*

If fot a courfe of years there has been no
fenfible increafe or decreafe in a place, thd
number of annual fettlers will be equal to
the excefs of the annual burials ibove the
annual births. If there is an incttaftj it will
be greater than this excefs* If there is a de^
creaftj it will be lefs.

The period of life at which thefe fettlers
temove, will appear in the bills by an in-
creafe in the number of deaths at that pe«
riod and beyond it* Thus ; in the LondoH
bills, the number of deaths, between 20 and
20, is generally above double> and between
30 and 40, near triple the number of deaths
between 10 and 20 : And the true account
of this is, that from the age of 1 8 or 2o» to
35 or 40, there is an afflux of people every
year to London from the country, which oc»
cafions a great increafe in the number of in-
habitants at thefe ages i and, confequently»
raifes the deaths for all ages aiove 2o> con-*

R a fiderably

*44 Of the Method' of forming

£derab1y above thetf" due proportion, ^ whea
compared with the number of deaths befort
20. — ^This is obferirable in all the bills of
mortality for towns with which I am ac-
quaintedy not excepting even the Brtjlaw
bills. Dr. Halley takes notice, that thefe
bills give the number of deaths, between 10
and 20, too fmall. This he coniidered as an
irregularity in them, owing to chance ; and,
therefore, in forming his Table of Obfcrva-
tions, he took the liberty fo far to corredl it,,
as to render the proportion of thofe who die
to the living in this divifion of life, nearly
the fame with the pi;oportion which, he fays^
he had been informed {a) die annually of the
young lads in CbriJi^Churcb HofpitaL But
the truth Is, that this irregularity in the bills
was derived from the caufe I have juft afiign-
ed. — During the five years for which the
Brejlaw bills are given by Dr. Halley^ the
births did, indeed, a little exceed the burials ;
but, it appears, that this was the eifeA of
fome peculiar caufes that happened to ope-
rate Juft at that time ; for, during a com-
plete century from 1633 to 1734^ the annual
' medium oi births was 1089 (^), and of bu-

{a) Sec Lowthsrp* % hhuigmcnt of the Pbilofophical
Triinfadiions, vol. III. p. 670. — Dr. Halle^ls information
in this inftance was not right, as will appear prefcntly \
mnd, therefore, he has by no means fufficiently correded
the irregularity I have mentioned.

(b) See Dfi Sh$rf% Comparative Hiftorjr, p. 63.

g^ rials

• Tables of Obferoations^ Sec. 245

rials 1256 (a). This town, therefore,- mu ft
have been all along kept up by a number of
yearly recruits froiD other places, equal to
aboat afeventb'^iztt of the yearly births.

r What has boien aow obferved concerning
the : period of life at which people remove
from tbe , country to fettle in towns^ would
^fiear- fbfikiently probable, were there \,o
f^ch evidence for it as I have mentioned ;
iw ft might be well reckoned, that thefe
people in general, muft be fingle perfons in
tfac! begifining ofmature life, who, not hav-
iBg yet obtained fbttlemeots in the places
where, theywere born,, migrate to towns in
qtteft of emplo}M9ients.

• • •

.' Haring premifed tfaefrObfervations, T (hall
Aekt endeavour to explain diftin^ly, the effedt
Which thefe accoflions to towns muft have,
on Tables of Obfervation formed from their
l)i}|fr of mortality. This is. a fubjed proper
to*be iofiftod on^ becaufe'miftakes have been
committed about it; and becaufe alfo, the
difcuffion of it is neceflary to (hew, hov^r near
to truth the values of lives come as deduced
frttH filch Tables.

«

(tf) It appears from the account in the Pbihfophlcal
Tr0ififSfim\y (Abridgment, vol. VII, No. 380, p. 46, &c.)
that*frbni I717 to 1725, the annual medium of births at
Ktejlaw was 1252, of bunals 1507 ; and alfo, that much
tfie greateft ' part o\ the. births died under 10 years of
age. — From a Table in Sufmilch*% works. Vol. I. p. 38,
it appears, that, in reality, the greater part of all that
die In this town arc childrcfn under five years of age.

R 3 The

Z4^ Of the Met M 0f forming •

The followii^ general nile may be given
on this fubje£):.

If a place has, for a courfe of years, been
maintained in a fhtte nearly ftationary^ as to-
number of iuhabitantSt by recruits comihgf in
every year> to prevent the decreafe that wpuUl^
arife from the excefs of the burials above the^
births ; a Table fornled on the princi]de^
^* that the number dying annually, after every
^^ particular age^ is equal to the number livw
*^ ing at that age," will give the number of
inhabitants and the proiyabilhies of life, too<
great for all ages preceding that at v^hicb t;^
recruits ceafe; and after this, it vv^l/^ve^
them right. — If the acceflions are fo gsaeat ft|:
to caufe an increafe in the place, fuch a Ta-*
Ule vf\\\ give the numbd? of inhabitants and
die probabilities of life, too httiey sfter dw
age at which the acceflions ceafe {a) ; aft^
too great, if there is adecrdafe. Bef^e thcK*
age it vviil in both cafes *give tUem ixm gre^t]'
but moft confidcrably fo in the ^mei C8if<^^
or v^hen there is an increife*

{a) Agreeably to thefc Obfervations i^ if a pliice fn-^
creafes, n6t tn confequence of acceffibns from other
places, but of a conftant excefs o£ tbe births abow ths^
deaths ; a Table, conftru^ed on the principle I hinro
mentioned », will give the Drobabiljte^ of life. tfi|Q low
through the whole, ixttnt of lifqi becaufe, in fucb cir-*
cumftances, the number of deaths in the JtrJH ftagcs^ o^
]ife muft be too great, in comparifon of the number of
deaths in the A7//^r ftages ^ and more or lefs (b» a^ thio
increase is more or lefs rapid. The contrary^ in all rc-
fpeSs, takes place where there is a decreafe^ arifing from
;t)e excefsi of the deaths above the hirtku

For

*'

Vfahies ,of Oh/ervatiinsi &c* 247

• For example. Let us fuppofe, that 244
of tbofe born in a town, attain annually to
ao years of age ; and that 250 more, all like-
wiie 20 y^rs of age, come into it annually
bom other places { i/i confequence of which,
it hai» iw 9 4ourfe of years^ been juft main-.
ttuned in the number of its inhabitwts, with^
oitf any fendble increafe or decreaie. In thefe
CtfcHQftftftnces, the number of the living in:
th^; town of the age of 20, will be always-
444 natives mm! 25P fettlersf or 494 in all ;
and, fince thefe are foppo&d all to die in the
tow0t and no morc^ recruits are fuppofed to
come in ; 494 will be like wife the number,
d^ifig annually at 20 and upwards.— In the
&it)c manner 5 it will appear on thefe fup^'
pofitions, that the member of the living, ztk
every age, fubibquent to 20, will be equal ta
the; number dying annually at that age and
above it ; and, confequently, that the num^.
btr of inhabitants and the decrements of life,*
&r every fuch tge^ will be given exadly by
the Table I have fuppofed. But for all agea
brfare 20, they will be given much too great.
For let 280 of all born in the town, reach.
10. . In this cafe, 280 will be the true num-*^
ber of the living in the town, at the age of
10 1 and the recrvlits not coming in 'till 20^.
the number given by the bills, as dying be*
tween laand 20, will be the true number,
dying annually of the living in. this diviiioA'
of life. Let this number be 36 j. and it will

R 4 follow^

248 Of the Method of forming

follow, that the Table ought to make the
numbers of the living at the ages between 10
and 20, a feries of decrtfafing nieans between
280 and (280 diminished by 36, or) 244*
But in forming the Table on the principle I
have mentioned, 250 {the number above 20
dying annually in the town who were not
born in it) will be added to each number in
this feries; and, therefore, the Table will
give the numbers of the living, and the |>ro«
'babilities of life in this divifion of life, almo^
twice as great as they really are, — This ob*
fervation, it is manifeft, may be applied lo
all the ages under 20.

It IS neceifary to add, that fuch a Table
will give the number of inhabitants, and the
probabilities of life, equally wrong before %o^
whether the recruits all come in at 20, agree-^
ably to the fuppofition juft made, or only
begin th^ to come in. In thislaft cafe, the
Table will give the number of inhabicants,
and probabilities of life, too great througbont
the whole ejstent of life, if the recruits come
in at all ages above 20. But if they ceafeiat
any particular age, it will give them fight
only from that age; and before, it will err all
along on the fide of excefs i but lefs confi"-
dcrably between 20 and' that age, than be-
fore 20.' " - For example. If, of the 250
I have fuppofed to come in at 20, only 150
then come in, and the reft ^ 30 ; the num-
bers of the living will be given 100 too. high,

at

Rubles (^ Ohfervations^ &c. 249

at every age between 20 and 30 ; but, ^s jufk
ibewii,. they will be given 250 too high at
every age before 20.«— In general^ therefore,
the number o{ the living at any partieular
age, muft be given by the fuppofed Table^
as aiany too great as there are annual fettlers'
after that age : And, if thefe fettlers come ia
at all ages indifcriminately, during any cer-
tain interval of life ; the number of inhabit
tants and the probabilities of life will be
fxmtifiually growing lefs. and lefs wrong, the
nearer any age is to .the end of that interval.
-"T^heie Obfervations prove, that Tables of
Observation formed in the common way, from
biUs of tBortality for places, where there is
ani excefa of the foiriials above the births,
muft be ^erroneous, for a great part of the
doraiion of life, in proportion to the degree
of that excefs. They ibew likewife, at what
parts of life the errors in fuch Tables are moft
Qimfiderable, and how they may be in a great
HEttaftire corre&ed.

All this I (hall beg leave to exemplify and
iUuftrate a Httle further, in the particular cafe
of London.

The number of: deaths, between the ages
of 10 and 20, is always fb fmall in the Lon--
don bills, that it ii^ms certain few recruits
come to London under 20; or at leaA not fo
many as before this age are fent out for edu«
cation to fchools and univeriities« After 20,

great

25^ Of the Mttbedoff^rmh^ ^

groat Aumbers come in 'rill: 30, and fonrie
perhaps 'till 40 or 50.-— But, at every ag^
after 50, h is probable, ihat more retire from^
Xm^ than come to it.*~The London Tablea
of Ohfcrvation, theirefore, being formed on.
the principle I have mentioned, cannot givae-
the probabilities of life right 'till 40. fie- .
t ween 30 and 40 they muft be a little too
high \ but more ib between 20 and 30 j^ and'
fnoilof all £> before 20.-*-It follows alfo, that
thefe Tables mufl: give the number of nfaa* •
bitants in London much too great*

Table XII, in the Appendix, it
ed in the manner I have explained; from the
LondM biib'^ 10 years, from 1759 to 1768 ;
and adapted to a iooo born as a radix^ The;
fum of the numbers in the jfecond coiumfi,.
dinrinifhed by half the number born, is t^j§^*)
According to this Table then, for every^ 1 000^
deaths in Lond^nj, there are 2$i as mdiay in«>
habitants ; or, in other wovds^ the ex p edtatkm'
of a child juft born is 25^ 1 and the inhafaU:
tants are to the annual burials, as 25^ to i^
'^-Bi^ it has appeared; that the nambers in
the fecond column being given on the fiip«
pofition, that all who die in London were born
there, muft be too great ^ and we have from
hence a demonstration, that the probabi-
lities of life are given in the common Tables*
of London Obfervations,. too high, for» at ieafty
the firft 30 years of life ; and alfo, that the
number of iubabitants in London muit be lejl

than

TaUts ^ O^ervationSf Sec. 251

tfatn 251, multiplied by the annual burials.
-r^Tlie common Tables, therefore, of London
Obferwitions,, uodoubtedly vnxit to be cor-*
reded {a) f and. the way of doing this, and
in general, the right method of i^ming ge*.
ixmne TiUes of Obfervation for towns, may:
be learnt firom the following rale*
* . ^' From the fun of all that die annually,
^' i^ttr any given age, fnbtrad the number
^ oi annual feltlers after that age ; and the*
^( remsunder wiil be the number q£ the liv*
** ing at the given age."
' This rule can want no explication or proof,
tftsr what has been already iaid.

if, therefore, the number of annual iettlers
in a town at every age could be ascertained |
a perleft Table of Oblwviitions: might be
formed for that town, fvom bills of mortality,
cAotainii^ an account <^ the ages at which
attdv init^ . But no more can be learnt in'
thia inftance from any bills, than the whole
nvmber of ammal Jettkrs^ and the general
divifion of )ifb in which they enter. This^
however, may be fufficient to enable us to
fonm Tabks that (hall be tolerably exad.-^

(#) The iagsniovs aad sccurate Mr. Simpfm Uw tbali
it WSJ neceiTarj to corrtd the Lmdm Tables, and be hat,
done it with great judgment ; but, I think, too imper-
fediy^ and without going upon any fixt principles, or
OieiBiiig particuladjr, how Tables of Obfervacioa ought
tp be foroofMi, and bow far ia different circuoiftaiices, and
at difFerent ages, they are to be depended on.

For

Z52 Of the Method ^f forming

For inilahce. Suppofe thfe annual deaths - in •
a town which has not increafed or decreafec^
to have been fbr many years^ in the* prx^)cr«»
tion of 4 to 3'. to the annual births. It will
hence follow, that i of the pevfons who- .die
in fuch a toivn zmfettlersy or ''emigrants from.
other places ; and iK>t natives: And the fud-*
den increafe in the deaths ^after so, will alfo
ifaew, agreeably to- what wacr before obferved, *
that they enter after thisiage* In forming
therefore a Table, for fuch a town, a quar^
ter of all that die at all ages throughout the
whole extent'Of life, muft he deduced, from
the fum of ajQ that die after ^very given age
before 20 ; and the remaind^ will be^ the
t^ue number living at that givenrage. 'And;
if, at ao, and every iage above it, this .dc-
dudion.' is .onnitted, or the number of tW
living at every Aich age is taken the fame .
with thefuoi of all that die after it, tberrd«*.
fttlt will be (fuppoling vin^^^the feitlerstd'
con3e in befot^e 3Q, and e?// before 40) aiTa^
ble exadt 'till 20; too* high between 20: and
30; but nearly right for fooie yeajs befiare
40 ; and after 40 ex ad agaiki.~*Siich a TaUe,
it is evident, will be the iame with the Ta-
ble laft defcribed at all ages above 20 j and
different from it only under 20. — It is evi-
dent alfo that, on account of its giving the
probabilities of life too great for fome years,
after 20, the number of inhabitants deduced
from it tnay be depended on as fomewhat

greater

TSles of Obfiroathns^ &c. 253

greater than the truth ; and more or lefs fb« as
the annual recruits enter in general later or
fooner after 20.

Let us n€^w confider, what the reiult of
thefe remarks Vill be, when applied particur
larly to the London bills.

It muft be here firil obferved, that, at le^
one quarter of all that die in London zxtfet tiers
from the country, and not natives. — The me-
dium of annual burials for 10 years, from
1759 to 1768, was 242,9565 of births 15,710,
The excels is 7246 ; or near a third of the
burials. — ^The fame excefs, during 10 years,
before 1750, was 10,500; or, near ift^ij^ the
burials. London was then decreajng. For the
laft 1 2 or 15 years it has been increafing. This
excefs, therefore, agreeably to the foregoing
obfervations, was then greater than the num-
ber of annual fettlers ; and it is now lejs. I
have chofcn, however, to fuppofe the num-
ber of annual fettlers to be now no more than
a quarter of the annual buriah, in order to al-
low for more omiflions in the births than the
burials ; and alfo, in order to be more fure
of obtaining refults that ihall not exceed the
truth ♦

Of every thoufand then who die in Lon-^
donf only 750 are natives, ;and 250 ^t/et^
tiers, who come to. it after 18 or 20 years of
age ; And, coniequently, in order to obtain
from the bills a more corred: Table than the
i2th in the Appendix, 250 muft be fub-

tra^ed

254 Of the Method of forming

traded from every one of the fiomber^ ih the
fecond column 'till 20 ; and the rtumbers in
the third column mud be kept the fame> the
bills always giving thcfe right.*— After 20,
the T«t>le is to be continued unaltered i and
the refult will be, a Table vtrbich will give
the n^mibers of the living at all ages in Lan-
\ion much nearer the truth, but ftill fbme-
vhat too high.— ^Such is the 13th Table in
the Appendix,— The fum of all the mimbers
in the fecond column of this Table, dimi«
niihed by 500, is 20,750. For every 1000
deaths, therefore^ in London^ thire are, ac«»
cording to thi€ Table, 26,750 living peribns
in it ; or for every fingle death, 20^ inhabi*
tants. It was before £hewn^ that the num-«
her of inhabitants in London could not be (b
great as 25 times 7 the deaths. It now ap^
pears^ (fince the numbers in the fecond cxh
lumn of this Table are too high) that the
number cf inhabitants in London cannot be
fo great as even 20 times 7 the deaths. And
this is a conclufion which, I believe, every
one who will bellow due attention on what
has been faid, will find himfelf forced to re-<
ceive. It will not be amifs, however^ to
confirm it by the following fa^, the know*
ledge of which I owe to the particular en^
quiry and kind information of Mr. Harris^
the ingenious mafter of the Royal Mathema^
tical School in Chrift-Ghureh Hofpitil.-i-
The average of lads in this fchod has^ for 50

7 yean

Tables of Ohfervdtians^ &c* 255

years paft> been 831. They are admitted at
ail ages between feven and eleven i and few
ftay beyond 1 6* They arc, therefore, in ge-*
neral, lads between the ages of eight and 16^
They have better accommodations than it
can be fuppofed children commonly have ;
and about 300 of them have the particular
advantage of being educated in the country. .
In fuch circumflances it may be well reck-
oned that the proportion of children dyiitg
annually, muil be lefs than the general pro-
portion of children dying annually at the iame
ages in London. — The fa£t is, that, for the
laft 30* years, i It have died annually ; or one
in jo\.

According to Table XIII, one in 73 dies
between 10 and zo, and one in 70 between
•eight and 16. That Table^ therefore, « pn>*
bably, gives the decrements of life in London^
at theie ageSi too little, and the numbers of
the living too great : And, if this is true of
thefe ages, it muft be true of all other ages
under 20^ and it follows demonftrably, in
conformity to what was befose (hewn» that
more people fettle in London after 2o» than the
.quarter I have fuppofed j and that from ao
to at leaft 30 or 35, the numbers of the living
are given too great, in proportion to the de-*
crements of life.

In this Table the numbers in the fecond
column are doubled at 20, agreeably to what
really happens in London ; and the funo of

the

256 Of the Method of forming

the numbers in this colamn dituinKhed by
half the whole number of deaths, gives the
expeSiation of life, not of a child juft born,
as in other Tables, but of all the inhabitants
of London at the time they enter it, whether
that be at birtl^, or at 20 years of age. The
expeSlationSy therefore, and the values of Lon--
don lives under 20, cannot be calculated from
this Table. But it may be very eafily fitted
for this purpole by finding the number c^
births which, according to the given decre-
ments of life, will leave 494 alive at 20 1
and then adapting the intermediate numbers
in fuch a manner to this radix, as to preferve
all along the number of the living, in the
fame proportion to the numbers of the dead*
This is done in the 14th Table in the Ap*
pendix ; and this Table may, I fancy, be re^
commended as better adapted to the prefent
ftate of London than any other Table. The
values of lives, however, deduced from it,
are in general nearly the fame with thofe de-
duced by Mr. Simpfon^ from tht London bills'
as. they flood 40 years ago. The main dif^
ference is, that after 52, and in old age, this
Table gives them fomewhat lower than Mr.
Simpfon's Table.

It has fufRciently appeared, what judgment
we are to form of the values of lives thus
deduced. During the greateft part of the
interval of life, in which the annual recruits
that keep up London come to it, thefe values

err

babies of Obfervdtionsi &k. > 857

fcrr on the fide of excefs : and after that in-
terval, they err, perhaps, a little on the fide
tJ^i defeSl {a) on account of retirenients froni
London in the laft ftages of life^

The

t.

, {a) I haie not taken i;«to account the efFefl of nnigra-;
iion%from tpwns, on Tables formed in the manner I have
explained ; becaufe, towns in general being kept up bj^
tecruits from the 6oufttry, the migfatiorrs^^fn them ard
of little confequence, compared with tfat migrations i9
them. — Thus ; in London, it appears from the mucti
greater number of deaths between 40 and ^o, than in
!any other ec^ual iifterval of life after 16, that liiore peo-^
pie come to re than leave it, at 6very age betvireen zo and
50* After 5O9 it is probable, that the contrary happens,
But, it (hpuld be confidered, that imi^anis from Lori-
1)0N after 50, are chiefly perfons whc/,' having got for*
tunes in bufinefs, chufe to leave off, and to fpend tha
latter part of their lives in country retirefnfents. But
iiov^ few are the(e conipared vvich the multitudes whcT,
tho' poflefled of good fortunes, never retire ; and with
the bulk of the inhabitants in toN^er Rations, who never
can hri able, without the gfeateft fncanvem'encie^, to quit
the Tenements by which they are fifpported ? It is,* how-
ever, likely, that retiretbents from LoffD6N are now
linore numerous than thev ever were ; and that they hav^
fitiu tfkOi on the bills or mortality, and oh Tables formed
froiA them ; by caufing theie Tables to gi^e the number
of the living too little, in conlparifon with the decrement^
of life, at every age^ from tltat art whichr the mfgration^
to znd from LoKdon become e<|uaf, to the age at whichr
(he latter ceafe.-^Td e^tpfafin this $ let ti fi^pofe, that
Hone fettle in Londqk after 50 i but tfattt, b4t«reen 2$
&nd 50, as many come to rt as retire fronrt it at all ages
^fter 35 ; »nd that thefe r^cirement3 ceafe at 70. In thi^
cafe, the Tables will give the proportion' of the livin|^
to the decrementa of life too high '//// 35. At 35, thrt
f ropmrtion will bt given right, J/tir 35, it wiH begin

S ca

858 Of the Method of forming

The number of inhabitaats in London may
alfo be learnt from what has been offered,
more nearly than by any method which hat
been hitherto. taken. It cannot, it has been
fhewn, exceed 20 times i the number of An-
nual deaths. Could, therefore, the annual
deaths be afcertained, we (hould know thfc
number of inhabitants within pretty narrow
limits. But the omiflions in the bilk are
fuch, that it is not poilible to afqertain, with
exadnefs, the annual deaths. Dr. Braken-^
ridge fuppofed thefe omiflions to amount to
2000 annually. The refult of a very minute
enquiry by Mr. Maitland is, that in the year
1729, they amounted to 3038. But they
are probably now much more confiderahlei
than either of thefe writers have reckoned

to be given too low ; and this error will increafe *dll 50 \
from which age it will decreafe gradually 'till it vapi&e^
sit 70 : And after 70, the Tables will be exadlj right
again.*- >This is the exad ftate of the elFed of retire^
ments from Londa^i^ on the London Tahle of Obfervations*^
But this eiFcd appears, indeed, to be inconfiderablej fot^
after 50, the values of lives by the London Table, are'
continually approaching nearer and nearer to the (kmc
values by other Tables ; which could not happen vcrQ
retirements attended with any grtat efFc^.— It is proper
to add, that in fumming up, as above explained, the
numbers of the living, ia order to find the number of
inhabitants in Loudon^ the circum (lance that thefe num- .
bers may be too fmall fur fome years after 40 or 50^ in
conftqueuce of retirements, is, undoubtedly, .much more
than balaoced by their being givcA^ too high betvtceA 20.

.7 them

Tables of Oifervattons^ &c. 259

them {a). Let them be 6000 $ and the num^^
ber of inhabitants will be 601^750 at moft.

All the preceding Obfervations are^ it i4
plain» applicable to bills of mortality for
towns in general ; and point out the way of
deducing from them genuine Tables of Ob^
fervations, which fhall give the true proba^
bilities and values of lives, and the true num-*
ber of inhabitants, in the town whofe bills
are given.*— I (hall beg leave to confirm and
lilttfirate this, in the particular cafe of the
town of Northampton*

In this town, containing foUr pariflies,
namely. All- Saint s^ St. Sepulchre s^ St. Giles ^
and St. Peter's, an account has been kept ever
fittce the year 1741, of the number of males
and females that have been chriftened and
buried (DiiTenters included) in the whole
town. And in the parifti c^ All-faint s^ con-
taining the greateil part of the town, an ac«
count has been kept ever fince 1735* of the
ages at which all have died there*

In 1746, an account was taken of the num-
ber oiioufeSf and of inhabitants in the town.
The number oi houfes was found to be 1083 ; .
and the number of inhabitants 5136.— In the
parishes kA All^atnts and St. Giles, the num-
ber of male zxy^ female beads of faaiilies, fer^

{a) Vid. Preface to a Collcaion of the Bills of Mor-
tality fr^ 1657 to 2758, p. 4, &c«

S a vants$

2 6o Of the Method of forming

^antSy' lodger s^ and children^ were par'ticularTy
diilinguiihed. — The heads of families were,
707 males; and 846 fctnzlcs.'-'^^^Cbildren,
males 6245 females y^g. '^Servants, males
^203; fenriales 280. — Lodgers, males 1371
females 287. — In St. Peter s, males 99 ; fe-
males 129. — In St. Sepulchre's^ adults 638 1
children 427. In this paridi the fexes were
not diilingui(hed.

The Chrijlenings and Burials in the whole
town for 28 years, from 1741 to 1770, have
been as follows.

Chriftcncd { J?jJ^^* ^361 1 4649— Annual mediatn 155
B"««» { Km.' aS^S } 5747-Annttal medium 191

In the parish oi jUl'Saints^ from 1735 to
1770, or 36 years,

ChriftenedJJ?"^,^ J J3J J 3242— Annual medium 90
Buried \ 1^^^' J§56 J 3690— Annual medium 162-J

Of thefe died.

Under 2 years of age — 1206

Between 2 and 5 — 276 ^^

Between 5 and .10 — 155

Between 10 and 20 — 155

Between 20 and 30 — ^ 297

Between 30 and 40 — 257

Be-

TnSIes of Obferodtions^ &c. 26 1

Between 40, and
Between 50 and
Between 60 and
Between 70 and
Between 80 and
Between 90 and 100

50 —

297

60 — .

300

70 —

293

80 —

285

90 —

^SS

00 —

14

Total

3690

A Table formed from thefe data in the
manner of Table XII ; or, on the fuppofition^
that all who die in Northampton were born
there, would give the expedation of a child
juil born 28.83 years; or, the proportion of
the inhabitants to the annual deaths, as 28.83
to r. It has been (hewn, that this propor-
tion, in a. place where the burials exceed the
births, muft be greater than the true propor-
tion of the number of inhabitants to the an-
nual deaths : And this appears to be the real
<:afe. For the bills (hew, that, from 1741
to i75P» or for 10 years, about the time
when the number of inhabitants was 5136,
the annual medium of burials was 197.5;
which, multiplied by 28.83, gives 5693; or
a 9th part more than the true number.

A Table formed in the manner of Table
XIII, would give tlie proportion of inhabi-
tants to the annual deaths, as 26.41 to i ;
and this makes the inhabitants 5216; or
very near the true number.

S 3 The

26z Of the Metbcd df farming

The IVth Table, in the Appendix, is form-
ed in the fame manner witH Table XIV, for
London : And this is th^ genuine Table of
Obfervations for Northampton, from vrhich
may be calculated the true probabilities and
values of lives, at all 'age3» in that town.

At Norwich, bills of mortality, of the
fame kind with thofe in London and Norths
ampton, have beep kept for many years. I
haVe been favoured with a copy of ^tfe bills
for 3a years, from 1740 to^ 1769. . The an-^
Bual medium of chrtfieningsy during this pe«
riodt has; been 1057 [a)^ of burutis: i%q6.
And from hence, together with the account
of the numbers, dying in the fevera) decads
of life, • aftpr i o, I have formed l^ble V,
which j^ews the true probabilities of life is
this towa»

(<?} Ill this rtgifter all tbat die before bapttOv,* anA
alfo alfthat are born and die among ^ahn, Jtws, &c.
are omitted. There are alfo foitie other onlifli&ns ; and
ifhe true annual nri^diun) of births arvd burirfs mifft be
greater^ tbsHi cbeyarc glvsf» in tbe biUa. fin^tht^ nfH)
bave no cffe^ on a TaWe of Obfervations,. funpofiog
the pr9pbrtms of the birtRs to the buriajs, aha of t;he
numbers dying in th« different flaget of Iffe, gfvon right.
—It is pfoper I ibouid (nsntton fvrtber hcrr, that tiefa
bSls ghre onl^ the whole number of children dying un-
der 10, without fpecifyingthe numbers dying under two
years of «ge, between 2 and 5, and between 5 and 10,
9S in other bills. I have, therefore, in foroitng die Ta«
bk for NoitwiCH, fuppofed the pfoportionsof iheff ntun*
bcrs the Umt that they are at Kortham? ton.

The

T^abks tfObJervatkns^ &*C, 263

The following particulars fectn to deicrve
notice here.

. Firft. Had thefe Tables been formed
from the Northampton and Norwich
bills^ for no longer time than any 1 o yeapf
taken together, of the periods I have men-»
tioned; they would have given the values
of lives nearly the fanie. Thefe Tables^
therefore^ are founded on a fufHcient num-*
ber of Obfervations ; and it appears, that
there is an invariable law which governs
the wafle of human life in thefe towns,-—
The fame remark might be made concern-^
ing London {a). See p. 256.
. Secondly. An account was taken at
%¥i^i.vi%^\i^Y^ in 1750J of the ijiibole num*

{a) Some have entertained a veryvrrongiiotlonof the
imperfeflions in the London bills. They do, indeed*,
give the vohrie number of births and deaths much too lit^
tie ; but the conclufions with rerpe(^ to the probabilitifef
of life in LaNJ>oN, and the proportion of inhabitants
dying annually, depend only (agreeably to the obferv^
tion in the lair note) on the proportions of the numbers
dying in the Taveral divifions oi life.; atul thefe are givea
ttgii in the IrONx>0N bills. — For firft, Xhere feeofis no^
thing in thi« cafe, that can be likely to caufe the deficit
encies iii the bills to fall in one diviuon of life more than
|n another :,fi^iu what decides thi« point is, that thefe
pri^>oruon5,> as given by the bills for any ten, or even 4;gp
five yearf, come out nearly the fame v^rith one another ^
^^d always very different from the proportions given<by
iDther bills.— There are no other variations, than fuch as
nm^ arife from the fluduations of London, as to ia«>
^eafe and decreafe ; and alfo from fome improvemetu^
In its ftate, which have lately taJ^capJace. See EiTay.L

p. Xqiy 192, 204. ' ^ r

S 4 ber

^64 Of^tbe Method of farming

htt of iDfaabitants ; didinguifhing, partlcakf ?
Jy, the number at the age of 21 and up-
wards. — U^he former number was 81 411
and the latter^ 5 1 87.rr-According to a Tar
blc formed for North AMPTONi in the fame
manner with Table XIII, for London, tbj
whole number of the living is to tiie nura*r
ber of the-iiving at 2 1 and upwards, as 26,41 f
to 16,5865 that is, as 8141 to 5113- — Ac-
cording to a like Table for Norwich, thcfe
numbers are to one another, as 24,500 to
i5,6Hoj that is, as 8141 to^52ro. — Thcfe
Tables, therefore, give the proportion of the
whole number of inhabitants, to the number
Df the living at 2 1 and upwards, almoit: cxr
a&ly the fame with the true proportion, as
it is at Shrewsbury {a) : And this af^rds a
kind of demonflration of the redtitude of the
principles op which thefe Tables have bcf^
formed*

In theparifti of Holy-Cross nearSHREws-
SURY^ an account was taken in 1760 an4

{a) The annual medium of Wrths at Shrews^uiiy,
for 7 years, from 1762 to 1768, was 301 ; of buriiala 329^
It appears, therefore, that otie in 244 of t|ie inhabitants
8ie annually. But it fhould be remembered, that in 1766^
the fmalKpox and meafles increafed very much the mor-
tal itv in this town ; and I find alfe, that, Tmce 1750, a
huwry {orfounMingshomhoiipw^ was eftablifiiea here;
and that in 17^8 this nurfery contained 660 children and
fervants. It feems, therefore, probable, that the true
medium of burials about the year 1750, inuft have bceii
lefs than 329.; and that the proportion of inhabit^t^
dving annually, m^y not be mutti greater than it is at
NoaTHAMPToNi or I in 26.41.

^fibles of Ohfervations^ &c. 165

f*7«ro, of the whole number of inhabitants i
|iiftingui(hing9 both times^ the number at tha
fige of 70 and upwards i and the laft time^
the number at 10 and upwards: And I find^
Ithat a Table formed from the Regijler of this
parifby mentioned p. i93» i94» gives, likewife,
ibe^ numbers as nearly the fdme as could
poiflib]y be expedSied.

But further .-^The nunriber of inhabitants^
not reckoning children^ in the parifhes of St.
Giles zxid AU'^ Saints i Northampton, was^
ki 17469 2460 ; and the whole number of inr
habitants in thefe. two parijhes^ was. 3*843^
Seep. 259."-^In the.account I have received^^
the particular age at which the lioiit oi child--
hood was fixed in taking this furvey, is not
mentioned ; but there is fufficient reafon to
believe, that it was 21 : And, taking this for
granted, the number of inhabitants, not chil-
dren, will come out, (by fuch a Table for
Northampton, as Table XIII for Lon-
don) 2414; or, nearly the fame with the
zuimber really found in thefe pari{hes««-<-Had
this pumber been computed, from a Table
formed forNoRTHAMPTON, in the manner of
Table XII, jippendixt it would have come out
only 2 1 76. This remark is applicable to the
Table for Brejlaw^ formed by Dr. Halley^
compared with the fame Table, correiflcd for
^11 the ages under 20 (tf), by the rHle| p- 251.

The

{a) I have given T>t. HaUi/% Table in thf? Appendix
juft as be framed it. A correction oi it oiigbt>e made
^ \ * from

9

s66 Of the Method of forming

The neCeflity^ therefore, of that ccrredion h
verified by fa&s ; and it appears, abundantly,
that the Tables I have given for North-*
AMPTON and Norwich may be depended
on*

. But, thirdly. In comparing thefe two Ta-*
bles, it may be obferved, that there ia:a dif<^
ference between them in favour of NortH'^
AMPTON, fenoer djring there in childhood,
and mort in old age. The fame would be
iband to be trae» wtsre the North Amp toh
Table to be compared with a correded 6r£8«*
LAW Table. It appears, therefore, agree-*
ably to what might have been expe£trd, that
NORTHAMPTON, being a fmall town com-^ '
pared with Breslaw and Norwich, is lefs
unfavourable to health and kingevity. TiM^
difterefice, however, is not confiderable. Af«-
ter the ago of 20, there is a ftriking confor-
mity between all the three Tables, which
gives thon great weight and authority.

t^urthen It ought to be particularly no«
ted, that thefe Tables prove the decrements

from the proportion of births to burials, mentioned p. 244.
And it would thtn appear, that a 25th part of the loha*
bitants at Brejlaw die annually^ and that half the num^
ber born die there under fix, as welt as at Norwich^ This
Table, as we now have It, makes half live to 16 ; but
the account mentioned in the note, page 245, (hews this
not to be the truth. It likewife makes the number of
inhabitants at Shrewsbury, above the age of 21, to be
47 JO; and in the pariihes of Jit- Saints and St. GiUsy in
Northampton, 2230. It gives, therefore, thefe num-
bers wrong i whereas, as obferved above, a correded
Table would give ctym true*

of

tables of QSjervatwns, &c. 26 f

cf life in moderate towns, to be nearly e^ual
thro* moft of its ftages. At Northamp-^
TON it appears diat, of a given number of
perfons alive at 20, the fame number die
every year 'till yS, without any interruption
worth notice, except between the ages of
^ and 40.-~A like uniform dccreafe in the
probabiUties of life appears in the Bresl aw
and Norwich Tables; but not fo remark*-^
ably. It was this circumftance in the Br£s-
1 AW Table, that led Mr. De Mohre to the
Hyf^thefisj defcribed in p. 2f, and ib ofteit
mentioned in this work. — ^The values of lives,*
I have faid, deduced from this Uypothejis^
agree fo nearly with the (ame values deduced
immediately from the Tables, that it is fcarce-
\f worth while to diAinguiOi them. But that
every one may be able to judge of this -for
Kimfelf, I have calculated {a) the fbllowiji^
Table.

bf Mr. ntMn^

16.69
15.89
14.68

11.34
9^01
6.06

4'. 29

Valae of a life
«ttlKage

12

201

Reckon. ^Q

lereft at AQ

. fni. 50
60

70

75

By Breflaw
Tabic.

17.617
16.49
14.77
12.90
10.87
8.58

5-59

y Ntmith

By Northt^mp-

Tabk.

t$m TaMe.

17.48

17*20

16.41

^5-93

H'^S

14.85

13-36

13.10

n.13

11.25

8.54

9.02

5-99

6.26

4.86

479

(41) Every calcalatioa of thia kind may be made widioiit
jBocb bboar, by a rale explained in noce (O) Jfftmiix.

It

n6B Of the Methd of forming

\ It may be obferved in this Table^ that the

^ucSy by the Hypotbefis^ come nearer to tl^c

teuc values by the Northampton and

Norwich Tables, than by. (he Breslaw

Table I and alfo^ that^ before the age of 60,

they are all much higher than the values' for

the fame ages Jn London by Table X 9 the

inhabitants of London^ (as Mr. De Moivn ob*

Ibrves) being '* for eauies {a) too well knpwn^

** more ifliort-lived than the reft of mankind/*

••—The Hypotbifisp therefore, is by no means

applicable to London lives. It is proper to

add, that neither can it be. applied to the va^

l|aation of Country lives. — It appears, from

fbe xegifter of the parifh of Hdy-Crofs (^),

ihat the expe&atims of lives there are much

greater than t\^ expirations by xYit Hypo t be/is ^

ir— The expeSlation there of a life {/:)

At 20 is ^8. BjHypotb. 33. In J^ond. 28^

27 33.9 29.5 25.J

30 3a 28 23,6

40 25,7 2t ..... igjS

50 20 18 . . 16

60 14.5 J3 12.4

'70 10 8 8,8

ia) Doftrinc of Chances, p. 347.

SeeEfliayl. p. 193,194. — I hive m the Supphmeut
g^rpn the Table of Obfervations from whence thefe con-
ctufi^s are deduced la p. 263. a fad is mentioned,
which feems to prove, that 20 years is a period long
enough to affbrcl data in this cafe of fufficient authority.
It is, however, certain, that the fame regifler continued
10 or 20 years longer^ will afford data more to be 4c-
" ' on.

From

^abks of OhJerbalioASp &t. '26^

'* From this comparlfon it appears; that the
*Hypotbefis^ from 20 to 6o> gives nearly tlie

medium

(r) The expedation of a child juft born in this pariAi,

19 33. At NaKTHAMPTON, II54. At NoRWICH, 2}^

in London, i8. — In this pariib, i in ii dies at 80, and
upwards. In Northampton ^ x in 22. In Norwich;
1 in 27. In London ; i in 40. Sec Eflay L p. 202* '

I Will add, that the probabilities of life here, appear 10
be much the iame, with the probabilities of life amow
the minifters and profeiTors in Scotland. — This is a fa$
bf fome confequence ; and, therefore, I (ball beg leavte
to give a brief account of it. ' ^

■ The mean age at which the mirufters and piofofl^
enter into benefices and profeiTorfliips in St9tland^ is reck-
oned to be 27. Their number is 974. The eftablilh-
ment among them for providing for their widows, begun
on the 25th of March 1744 ; from which time to ATmcii^
bfT 22, 1770, 774 have died : That is; 29.07 annually;
or I in 334- The ixpe£iation^ therefore, of a life amonx
them, at the age of 27, is 334* ; which is nearly the fanie
with the expe£iati<my as given above, of a life of the fame
|ige in the pariih of H^fy^Croft i and 34. years more, ffaaa
the expeSfation of the fame age by Tables III, IV and V«
—Now, the ixpeSfation at a given age, being compoied
of all the probabilities of life from that ase to the eactre-*
mity of life -, there arifes from hence reafon for conclud-
ing, that the probabilities of life among the minifters in
Scotland^ cannot differ much in any part of life, from
tbofe in this parifb.— But there is another faft that con*
firms this obfervation. ,

The annual average of weddings among the minifters
and profeiTors in Scotland, for the laft 27 years, has
been 31. The average of married perfons amang'themf
for 17 years, ending in 1767, had been 667. This num-
ber, divided by 31, gives 214^ the expeSfation of marriage
among them ; which is above 24 years more than the
cxpe^ation of marriage would be, by Dr. Hal!e/s Table,
on the fuppofition, that all ift, 2d and 3d marriages may
be juftly confidered as commencing^ one with another^
fo early as the age of 3©.— The exfeSlation of two equal

4 joim

«70 Of the Method of forming

'medium between the expeSations of Londoit
and CouKTR Y lives i and for tbis reafbn itig
czcelleatly adapted to general ufe.^-^After 60^
the expeSlations and ^d^^^.^ of lives ia London
approach nearer and nearer to the exftStations
and values of lives in Northampton^ Norwich^
and Breflaw ; 'till^ at yo, they come to be
almoft the fame. This is a circomftance
which, I believe, has noC been attended to :
And it is the more furprifing, as there is no
caufe known, which can produce any error
in the values of lives after 60, deduced from
the London Table, except migrations from
London ; and the effect of tbefe muft be to
^minijh thefe values.

The following obfervations will, perhaps^
account for this.

It has been proved, that at Icaft ha^ the
inhabitants of London, turned of 20 years
of age, are emigrants to Londom^ from the

jmnt lives is to the expeSlatlm of % Jingle life of the ikmt
age, as 2 to 3, by note (L) Appendix. It follows, there-
fore, that among the miniiiers in Scotlandy the expe^ation
Q{%fingh life at 30, cannot be lefs than 32.25. Moft
probably it is more ; on account of the later commence-
ment of marriage in the fituation of the ZcQtch mini<-
jfters. — I reckon alfo, that 27 muft be lefs than the mean
age at which they enter their benefices and profeflbHhips ^
meaning by it, not the age on each Ade of which equa|
numbers enter ; but the age at which, the excefs of the
interval of time taken to enter on one fide, is juft fuch as
to compenfate the greater number who enter on the other
j^de. See the conclufion of note (Fj Appendix*

country.

Taiks ofOhfervaiians^ &c* a/x

joountiy* So great a change as that^ from
the country air and modes of life^ to the air
and modes of life in London^ 'mud be parti*^
colarly hurtful to tfaefe perfbns ; and, there*-
fore^ (except it^auts) it is in them, prabably^
that the pernicious influence of London on its
inhabitants chiefly takes place. They come
in at every age 'till near 50 ; and this is the rea*-
fon why the deaths continually increaie im
London 'till that age ; but, after that age, the
inhabitants confifting chiefly of perfons, who
(like aien tifed to drink) have httxx fe^^ned to
London^ or with whom it does not happen
particularly to difagree ; the number of deaths
becomes lefs, and the values of lives begin to
approach nearer to the common fl:andard in
imaller towns*

There is one morefaA which I fliall here
take notice of; and which deierves more ati-
teation than has been hitherto bellowed upon
it« I mean ; ^* the diflerence between the
^^ probabilities of life among males and fe*
** males^ in favour of the latter/'

From the account in p. 260, it appears, that
at Northampton, tho' more males are born
than females^ and nearly the fame number
die ; yet the number of living /^;:«^/fj is greater
than the number of maUs^ in the proportion
of 2301 to 1770, or 39 to 30. This cannot
be accounted for, without fuppoflng, that
males arc more {hort-livcd ihdin females. — One '

obvious

ty2 . Of fie Method dfforMng

obvious reafon of this fadt is^ that *males zxi
more fubjedt to untimely deaths by accidents
of various kinds. ; and alfo^ in genera]» more
addicted to the excefTes and irregularities
which (horten life. But this is by no means
the only reafon. For it fhould be obferved^
that at Northampton the number ofy^*
^ale children was, in 1746, greater than the
number of male children^ in the proportion of
759 to 624.— The greater mortality of males,
therefore, takes place among children. — But
this, together with the greater mortality in
.general of males at all ages, will more partir
cularly appear from the following recital of
fafts.

In the parifli oiHoly-Crofsy Salop ^ the inge*
nious Vicar, Mr. Gorfucby in 1 760, and again
in 1 770, took the number of male and fe-
male inhabitants turned of 70. In 1 760, the
number of females turned of this age, was
35; of males, 8. In 1770, ihefe numbers
were, females, 35 ; males, 26. And for the
laft 10 years, 11 out of 365 have died be*
tween the ages of 85 and 1025 and they
were all females.

' At Berlin, it appeared, from the accu»
rate account which was taken of the inhabit
tants in i747f and which has been mentioned
in p. 224, 225, that the number of female oiii^
zens exceeded the number oimale citizens, in
the proportion of 459 to 39 1 : And yet, out of
this fmaller number of males, more had died

for

7qbks of Obfervathns^ &c. 273

ft)t 2Q years preceding 1751, in the propor-
tion 9/19 to 17 (tf).

At Edinburgh, in 1743, the number of

females was to t;he hunriber oi mates ^ as 4 to 3 ;
(See'^ffay.L.p. z 1.5) but the females that died
annu^ly, frpm 1740 to 1758, were to the
i^^» in no ^ijgher. proportion than 3! to 3.
Before 1749, the bills gave the totals of bu-
rials» without diflinguifhing them into the
tot^fl^ of males and females dying every year.
Mr. Kerfeboom^ in his Effay on the num*
bers of people in Holland, informs us^
that from the Tables of afiignable Annuities
for lives in Holland^ which had been kept
there for 125 years, wherein the ages of the
per/bns dying are truly entered ; it appears,
th^t. females have, in a)] accidents of age,
lived about 3 or 4 years longer than the fame
number of males. See Fbilofophical Tranf^
aSiifins abridged. Vol. IX. p. 326.

In Volume^ the 7th of the Philofopbical
5/rtf«;&^w»^ . abridged. Part IV, p. 46, &c.
th^ is an account of the nun^bers of male

^z^ii, feiffale ilill-born children and chryfoms,
and of boys and girls undet 10, pf married

.men and married women, and of widows
and widowers,^ who died fqr a courfc of years
at Vienna f Brejlawt Drefden^ Lei^c^ Ratifbon,
and fome other towns in Germany.

{a) Vid. Sufmikhy GotiUcbi OrJnungy &c. where a mi-
nute ticcount is given of the nuober of male^ and females
* at Berlin in 1.747 > ^^ ^^^ ^^ ^^ numbers of each
fex that had died from 1722 to 1750.

T . He

H

«74 Of the Method affirming

• ••

He that will take the pains to examine
thefe accounts will find that, though in thefe
towns the proportion of males and female^
born is qp higher than 19 to i8» yet the
proportion of boys and girls [a] that die is
8 to 7 1 and thaty in particulars^ mt Jiili^born
and chryfom malesy are to the ftill-born an4
cbryfom fetnoks^ as 3 p 2.

In thefe accounts it appears alfo, that df
7279 married perfons who nad died in theie
towns (^), 4336 were married men^ and but
2934 married women ; that is, three married fneh
died to two married ipofnen.- — ^In all Pome-
JRANIA, during 9 years, from 1748 fo 1756,
there died I3>550 married men, and 10,007
married women; that is, nearly 15 to ij.
SufmilchfGottlicbe Ordnung;wo\. i. tables, p.97.
The fcheme for ^ making provifion for the
widows an4 orphans of the miniflers in
Scotland, has obliged them to ^eep an
account of the number of weddings among
them, and the number of widows left an-
nually ; and it appears, from . the reports of
$he fruftees fqr parrying this fcheme ii^to 9x8-

{a) Ifi tbo apcount) frpoi BnJJaw it i$ particularly

inentioncd, tbat^by boys and girb are meant children tQ

10 years of a^, of whom, for 8 years from 1717 to 1725,

jiven males died tOj/^ feiofd^i, ^^luliyely gt thtj^iU-b^n

and cbryfimsm

{i) In Briftmif alone, for the eight yeari mentioned ia
fhelaftnote, 1891 married men died^ to ii96marnp4
ffpmca y that is 5 to 3.

7 PUM,

fables of Obfervationsy &c. 275

Cution^ that the annual medium of ^weddings
{a)i is (as obfervcd in the note, page 269)
31. And the annual medium of widows^
who have come upon the fcheme for 27 years^
IS I g4. Of 3 1 marriages then contracted art-
nually^ 194 become extinA by the deaths of
bujbandi. ; and but r i .8 by the deaths of wives.
That is i among the xniniftcrs and profeffors
in Scotland, 20 married men die to 12
married women ; or 5 to 3. It appears, there-
for^, that there is the chance of 3 to 2, and
in fome circumftances eveh a greater chance,
that the woman (hall be the furvivor of a
marriage, and not the man. In order to ae-
'count for this by the difference of ?ge be-
tween men and their wives, this difl^rence
ought to be' at leaft 12 years [b). That isi
fuppofing the ^ean age at which women
marry to be 23, the mean age at which men
marry ought to be 35. But this feems to
jexceed the bounds of credibility ; and, there-

«

{a) The annual medium ofweddings, smong the mi-
nifters admitted to benefices, has been, for 27 years from
-^e cottmencemMt of the fcheoie, 27. fiefides thefe, I
find there have been 4 weddings annually among theiti,
iefifi ^AmSon to benefices- The wbokanau^ medium^
therefore, is no more than 31,

{h) The chance of furvivorlbip between two perfons
aged 91 and 34, is nearly 3 to 2 in favour of the former.
There is the fame chance of furvivorihip between 25
and 37 ; and 28 and 39, This may be learnt from Pro-
blem XVI, in Mr. De JIMvr/u Treatife on Lif^-^Jn^

T a forts

'ay 6 Of tie Met 60 J of forming

»

fore, very cirobably, the greater mortality of
males muit ppcrate in this cafe, ,

It is farther, p.bfervablp in the accounts from
[ Qerm4ny^f , to Mhii^h 1 hgvc, referred, that the
number oi/wuiows.^ifing annuallvy is four
tjmes jtbc, autfibei; of wuiowers {a) ; and, as
^ wuiom are certainly, one with another, feve*
ral ycar^ younger than widowers; it may be
concluded, from hence, that the number of
the former' in life together could not be lefs
than five times the latter.— This fadl is like-
ivif^ confirmed, by the obfcrvations which.,
have been>made among the minifters in Scot-'
Jap J. In J 77c, the number of widows in
,life, dfriyeflarom the whole body ,of rhini-
.llers and profefibrs, jyas 3S01 l)ut the nuin-
, bqr of ifii^iowfrs among the^n has, one j^r
with another, been fcarccly 90 ; that is, not fo
much as 19 quarfer of the numbec of widows. ^-^
.It m^y be eafily feep, ^nd it would not be dif-
ficult to dem^nftrate, that neither the greater
number of perfons left widows, nor any pro*

.t

i^a) In Drtfdm alone, the number of m'^^ii who died,
. \v\ fouryears, was 584. The fiumber of widmifirsy 149.
• That is; 4 to i;.»-At Wittenberg, during ii.ycais^
98 widowers died, and 376 tindows.r^At Gqtha» during
20 years, 210 widowers and 760 widows. Sufmikh*s Goi^
iliche Ordsmng^ Vol. II. p, 273. — In the countiy, on ac-
count of a lefs difiFenence between the ages of bufbanda
and wires and more early marriages, the deaths of wubw"
eri and widows come nearer to one another ; for 10 Po-
MERANisA, during the 9 years mentioned in p.' I74, the
widowers that died were 41 1, the widows 1553 ; or.2 to 5.

7 bable

Tabies of enervations p ^c. 27/

})able fuppofition concerning the greater fre-
jijuency of marriages among widpwers, can
completely account for this^' with(^pt admit*
ting the greater mortality of males. -^This,
therefore^ appears on the whole to be a fad
well eilablimed : And it follows from it, that
in order to calculate the values of Life-An^
nuities and Keverjions with cxaftncfs, there
ought to be diftinft Tables of the Pfph^bili-
ties of life for males znA females. All that is
neceflary to obtain the proper data for form-
ing fuch Tables is, that the /exes as well as

. the ages of the dead (hould be fpecified in the
bills; andi thi^ is an improvement of our
bills {a) of mortality which would give little
trouble^ and which, therefore, I hope, will
be fome time or other made,

It has been obferved, that the author of
nature has provided, (hat more males (liould
be born thznjemales, on account of the par-

. ticular wafte of males, occafioned by wars and
other caufes. Perhaps it might have been
obferved with more reafon, that this provi-
iion had in view, that particular vvenknefs
or delicacy in the conftitutioh of male6,

(m) This improvement would be reiulcred more com-
plete, by diftinguifliing the males that die, under (he de-
nominations of married nuriy widowers^ and haichelhrs |
f^l4 the/emaksy under the denoipinations of married ^o-
men^ widowsy and virgins. — The ufe 1 have made of fome
accounts of this kind which have been kept id Germany^
ihews fhac this w^uld be of confiderable fcrvice.

7 which

278 Of the Method of forming '

which makes them fnore fubjefl: to morta-
lity ; and which, confeqlicntly, renders it nc*»
ccffary, that mcirc oi them fhould be pro*
duced, iti order to prefer ve in the world a
due proportion between the two fcxes.

In the courfe of this ^flay, it has often
appeared, that I have been particularly in-
debted to an information which I have re-
ceived from Northampton.— I fliould bo
jnexcufable, did I not mention, that I owe
this inforn^ation to Mr. La^ton^ an ingeni-
ous gentleman in that town, who has pre-
ferved the bills of mortality there with much
care, and been very obliging in communicat-
ing them to me.*— It is much to be deiired,
that like ^ accounts were kept in every town
and pari(h. It would be extremely agree-
able to learn from them the different rates
of human mortality in different places, and
the number of people and progrefs of popu-
lation in the kingdom. The trouble of keep-*
ing them would be trifling ; but the inftruc-
tion derived from them (^), would be very
important.— I have already propofed one im-
provement of fuch accounts. 1 will add, that
they would be ftill more ufeful, did they give
the ages of the dead after i o, within periods
oi fve^ inflead of /^« years.— During every
period, fo fhort zsfve years, the decrements'

{a] See £i&y I. p. aio, aix.

of

Rubles, of Ohfirvationsy &c. 279

b£ life may^ in conflru£ting Tables^ be fafely
taken to be uniform^ Sut this cannot be
equally depehded on^ in periods fo long a$
ten years;

There is yet another improvement of tnelc
accounts^ which I fhall take this opportunity

, to mention. They fhould contain not only
a lift of the diftempers of which all die, like
that in the London oills ; but they (hould fpe-
cify particularly the numbers dying bf thefc
diflempers, in the feveral divifions of life {a).
Accurate registers of mortality kept in this
manner^ in all parts of the kingdom ; and
Compared with records pf the feafons, and of
the weathef> and with the partictilar circum-
ftances which difcriminate aifferent fituations^
might contributte, more than can be eafily
imagined^ to the increafe ef pbyjical know*
ledge. — But to proceed no farther in thelc
Obfervations 5 1 fhall now beg leave to (hut
up this whole work with the following ge-
neral reflexion*

■

I have rcpreferited particularly, the great

difference between the probabilities of human

life in towns and in country parifhes ; and

. from the fads I have recited, it appearsi that

the further we go from the artificial and ir-*

{a) Since the former editions of this work, bills, oh
en improved plan of this kind, have been a<9uatly efta-
blifhed ^x Mancbcfter and Ch^er*

T 4 regular

i8b Of the Method df forming-

regular modes of living in great towns, the
fewer of mankind die in the ^f;^ ftages of
life, and the more in its loft ftagcs* Tkt
lower animals (except fuch {a) as have been
taken under human managemient) feem in
general to enjoy the full period of cxiftencc
dlotted them, 'and to die chiefly of old age :
And were any obfervatlons to be made among
favagesj perhaps the fame would be found to
be true of them. — Death is an evil to which
the order of Providence has fubjedled every
inhabitant of this earth ; but to man it has
been rendered unfpeakably more an evil than
it was defigned to be. The greatcft part of
that black catalogue of difeafes which ravage
human life, is the off-ipring of the tender-
nefs, the luxury, and the corruptions intro-
duced by the vices and falfo refinements of

. {d) Calves are the only animals taken under our pe-
culiar care immediately after birth ; and, in confequence
of then adminiflring to them the fame fort of phytic that
is given to infants^ and treating them in other refpe<9s in
th^ fame manner. It is probable, that more of them die
foon after being born, than of all the other fpecies of
animals, which we fee in the fame circumftances. See
the Comparative Fieuf of the State and Facultiet of Man with
thofe of the Animal fforld^ p. 23. — It is, indeed, melan-
choly to think of the havock made among the human
fpecies by the unnatural cuJtom$ as well as the ^icet^ wbi^h
prevail in polifhed focieties. I have no doubt, but that
the cuftom> in particular, of committing infants, as foon
as born, to the care of fofter mothers^ deflroys more lives
than the fword, famine, and pefiilcnce put together. .

- • civil.

Tabks of Ohfervations^ ice. 281

civil fociety {a). That delicacy which is in-
jured by every breath of air, and that rot-
ten nefs of conftitution which is the eSkik of
indolence, intemperance and debauchery,
were never intended by the Author of Na-
ture ; and it is impoflible, that they ihould
not lay the foundation of numberlefs fufFer-
ings, and terminate in premature and mifer-
able deaths.— -Let. us then value more the
iimplicity and innocence of a life agreeable
to nature ; and learn to coniider nothing as
favagenefs but malevolence, ignorance, and
wickednefs. The order of nature is wife
and kind. In a conformity to it confide
health and long life ; grace, honour, virtue
and joy. But nature turned out of its way
will always punifli. Tie wicked jhall not live
out half their dc^s. Criminal exceifes em«-
bitter and cut (hort our prefent exijience ; and
the higheft authority has taught us to ex-
ped:, that they will not only kill the 6ody^
but thcjbu/; and deprive of an everlast-
ing EXISTENCE.

(a) The ingenious and excellent writer quoted in the
laft note, obferves, that the whole dafs of difeafes which
arife from catching cold, are found only among the ci-
vilized part of mankind, p. 51.'— And, concerning that
lofs of all our higher powers which fo often attends the de-
cline of life, and which is fo humiliating to human pride ^
he obferves, that it exhibits a fcene lingular in nature,
and that there is the greateft reafon to believe, that it
proceeds from adventitious caufes, and would not take
place among us if wc led natural lives, p. 62,

APPBN-

APPENDIX.

Note (A). See Queftion III. Page 1 1.

T £ T E be any girr n expectation of life ; and

'^^ ^ - ^ x px will be the number of perfons

alive at the end of x years, ariling from p perfons
left annually as widows, (or added annually to a
town or fociety) at the age whofe expeSation is £•
The maximum^ therefore, is always ^E— * In Mr.
De Moivr^s Hypotbefts^ E is always 4 the diflference
between the given age and 86. See the note, page 2^
and the latter end of the note in page 37. See
likewife the beginning of the Firft Eflay, and note
(L) in this Appendix, where the inveftigation of
this rule will be given.

It will not be amifs to give the following ex*
ample of the application of this rule.

At the time of the commencement of the
fcheme, among the minifters and profeflbrs in
Scotland, for making provifion for their widows
it was neceflary, that a calculation fbould be made
of the number of widows that would be upon the
fcheme at the end of every year, till they came to
a maxiffmm^ on the fuppoficion that, (agreeably to
what particular enquiry had (hewn to have hap*
pened for many preceding years,) 20 new widows
would be left every year [a). In order to make

(0) For the laft 27 years ; that is, from the commencement
^the fcheme to the prefent time* Uiii number h^s been i9j»
a$ meationedy p. 275.

tha

4^4- APPENDIX.

this calcuktion, let 4 of the 20 widows be fuppofed
to be under 32 years of age when left ; and kc 2S
be fuppofcd theii: mean^age* Lee the fame num-
ber be left between 32 and 39, and let 35 be their
mean age; between 39 and 47, and 43 their mean
age; between 47 ttnd S7y ^"d 52 their mean age;
between ^y arid the extremity of life, and 63 their
mean age. The number in life together, to which,
'in 10 years, 4 widows left annually at the age ef
28 will grow, is, by the rule, (E being i'^)

' X 40, or 36.55. The number alive at

the end of 20 years^ will be ■ 'X 80, or 66.24

At the end of 30 years, the number alive will be

89 ; of 40 years, 104.82 : of 58 years 116

Thefe numbers, found in the f^me way, for the 2d
clafs, (E being 25.59) at the end of 10, 20, 30, 40^
and5i years, will be 36.7— 64.31 — 84.7 — 97.25—*
102 — T-For the 3d clafs» (E being 21 .5) at the end
of 10, 20, 30, 40, and 43 years, 35-34—61.4—
78.13 — 85.6—86 ■ ■ ■ F or the 4th clafs, (E being
17) at the epd of 10, 20, 30, .;^d 34 years, 34.11
—56.47-— 67— 68— —Fpr tb^ 5th clafs, (E being
11.5^ at the end of lo, 20, aiyl 23 years, 31.3-—
45.2— 46— —The whole number, therefore, con-
fiftiog of aJi the claflfes^ will come to a m/txifnum
nearly in 58 years ; and tji^ totals in life, at the eqd
of 10, 20, 30, 40, 50, And 58 years^ will be
^73-37— 293-58— 364,83—4Q|*67t-:4i8.

Thefe defiermi^a^ioos fpppQfe op^e to many.
In 10 years, from 1757 ;tp 1767, I Ipjave been in-
formed, that bmt 9 widows n^ar/jied. Let us then
fuppofe, that one widow of the firfl: clafs marries
every year ; and let all that marry, be fuppofed
to continue, one with another, 5 years in Vidow-

hood

r

APPEND IX

285

hood before they marry. On thefe fuppofitions,
the'foregoing tocaU will» at ^e eod of the fame
periods of years, be 16^.%^ — 'ziz — 347.^—

380.47—394, . «-

r Thefe calculation^ are made from Mr, Ij^
JMoivre'% Hypothefis. Had they been made ea.-
a&ly from Dr. HaUef^ Table, or any other of the
'Tabies I have given at the end 6f dik work, ex-
cept the Lmdon one, the refults would have beem
very nearly the fame. ".."'*

' Twenty-feven . years hai^e now efopfed (ince tjbp
commencement of this fcheme \ and the numjbqr
irf widows living* every year have, in fa&, corres-
ponded to the laft numboB I have given, as nearly
M could be expede^t

Note

«86 A P P E N D I Xv

Note (B). Queftion VI. Page 21^
T ]£ T r fignify thejum of i A and its intereft,

for one ya/ir. The value of a life, whofe

lemeot is n^ being (by Mr. De Moivre dk

jinnuities^ 4th edition, . page 14. and p. 100^

^^ + !£^ + lz3 + lri, &c. the prefentva-
lue of the retnaiiHteii of it after two years muft be
J^+ ^, &c,; which is equal tp ^ X ~i X

Now -^ is the prcfent value of i /• due at the

end of two years, -« — ^ is the probability that t

life, whofe complement is n^ (hall continue two

years, and^=rr + «=?=-.+ =;r-, &c. a the va-

lue of a life two years older than the life whofe
complement is »• And, therefore, (fince any num«*
ber of years lefs than n may be fubftituted for two
years) the firft rule given in this Queftion is right.

The fame procefs, applied to joint lives, will
demonftrate what is faid in the ScboUum^

Notei

1

APl^fi^NDIX. 48^

Note (C), See Qucftlon VII. Page 22, '

LET the complements of any two aflSsnecl
lives be it and m. The prefent value of thm
firft poffibie [>ayment of an annuity to be enjoyed
fay the Ufe fehoie complement is n^ provided ioii
live^ CQttt\mtt 7 years, and the life, whofe comple«
inent is n^ furvives the other after thj)t terai, is the
probabili^, that i^he liJFe of t)ie expeftant fliaH
coatioQe 8 years, and th^ other life 7 yeary and

then fail in the 8th year, multiplied by -. , or by

1 /. difcounted for 8 years.'^^The probability that
the Hfe of the txpi^ant Ihall contmue i yeifs is

#_ •

;Xi . ■? r^ -=i"'> The probaljility, therefore^

The probability tjiat the other life fhall coi^

tinue 7 years is — ^. .The probability that it ihall

continue 7 years, an4 f^l ip the 8th year, is

tn — 7 ^^ * w— 8

m

tjbat the life of the txptHant (hall coptinue 8 yev^

s(nd the ptb|;r life continue 7 years and fail in the Sth^

w— 8 I
is ——X - \ and the prefent value of the firft po0i*

()le payment pf the annuity fuppofed, is — ;»x -•

vr fti

See T'it^ Do^rine of Annuities^ by Mr. Smpfim^
p. 6— ri5, or his 5i&5 Exercifesj p. 315, fee-
In like manner, the prefent value of the 2d pay-
mppt, at the ettd of the 9th year* may ba found

to

^8)

A P P E N ai Xj

to be

nr^

X X 1

m

— -^» or — -2 X -,

and the pr^nt value of all^he ppflible payments,

1 » — 8 I n — Q 2 . If— lo 1 ^

*' »r m «r w wr m

Btt thsfr'ieries is <qual to .^ x ^~ X 2Z^ jj^

I %i >■

^^■^••■i-WP""''*— *iii«i^

10

1 , n — 9 2

+

"a..

Sec. Is theWaTuc" of an annuity for -a Kfc (even
YcaoD c4(ikr f hbd • ^he . ex^i^ant^ aj^ f^^P^^- jjjp
feven ycar» older than the life whofe coflbpiement

11 tlie'probabUity t^^tboi^

the afllgneid hves (hail continue 7 jsears* And^

list the :«akie df Ji I due at thjc. end of 7 years*. Xhe
rule, therefore, given for folving this queftion. Is
^fight. . '

Thi^ detnonilration, as well as thac in the la^

* note, is, iot the fake of more eafe and cteaatie»,

e.appHcd to the, hypothefis of an equal decrement

e!Ofetife. It does, not, however, depend upon it,

.but tnzj be applied to any table of obfervations;

' i

Kott»

A'P'PENDIX. zSg

J^pte (D)* <^eftiDn IX. Page zg,

LET the complement of ^oyxwo allagacd lisses
Ije. If Md 4n^ acdisic ^jivt-ji 'term be fevm.
years, as in note*(C). .1 he probability that the
fdrmer life (fupppfed to be cIkt life in expectation)
(iiall lafl: 8 years, is, by Mr. De Alcivre's f-lypo-

tliefiB, *4.^ ; .ajid the probability chat the kttcr

n

g

life Aall fail in 8 years, is - ; and the firft pay-

ment of the annuity mentioned in this queftion,
depends on the happening of iofb thele events,

«•— 8 8
the probability of which is x -^

The prefent value, therefore, of the firft pofTible

g g

payment of the annuity is — — ■ x -.——In like

manner -, the prefent value of the fecond pofTible

payment is 2Z^ x - h and of all the payments,

n — 8 8 . n — g ^ o , h — lo *o © n ^

— r X - + —- X - + — — X — , &c. But

«— 8 8 »— 8 I , «— 8 ^ 7 , n — 9 ^

— T X - = — r X - + — r X - •, and -^ X

ries, therefore, is equal to the two feries's ^ X

a90 APPENDIX.

*

I «— 7 jw— 7 « — 8 I

tO;:; X •— ^ X -~ X =- X — — + ==^

- + ==— X -^, &C- + -7 X -^ X

j=r- + ^ 4- 3 &c. which IS the vcrjr

n — ^r n — yr* n — yr*

rule given for folving this queftioQ, as will appear
from notes (B) and (C).

Note,

n

APPENDIX. S9I

Note (E). See the Scholium to Que ft. X.

A C CORDING to the calculations, the time
JiX, in which the firft yearly payment of a rcvci'-
uonarv annuity becomes due, is the end of the year
in which the event happens that entitles to it, how-
ever little or much of the year may then happen to
be unelapfed. And this, likewife, is the time
vhen a reverfionary fum becomes due. Thofe who
kfiow how the calculations of the values of rcver-
lions are inftituted, muft know this. But an an-^
n6ity, the firft payment of which is to be made at
the lame time with another payment of a fum ia
hand, ftifficient to buy an equal annuity, is worth
one yearns purchafe more than that fum. For
ioftance. Reckoning intereft at 4 per cent, and r
being 1/. increafed by its intereft for ayear, or 1.04,

-+~-t-"-5j &c. = 25/. is the preient value cxf

an eftafe of 1 /. per annum for ever. That isj i% »
the' value c^ ic, fuppofing the firft rent of it is to

be paid a year hence, If the firft rent is to be

revived immediately^ or at the fame time With
another payment of 2$L it is worth one year*s
purchafe motCi or eqmvalent to 26 /. — — -I have
not found, that any ot the writers on annuities and
fevcrfiohs, have attended to this obfervation. Ic
fuggefts a correftion neceffary to be applied to the
common folutions of feveral important problems :
particularly to the 2 1 ft and 2 2 d in Mr . S imp/on* s Trea-
iife 4m Annuities^ and the 26ch, 27th, 32d, 33d, and
40th problems in his SeUSl Exercifes ; and to adl other
problems of the fame kind in other writers. There

U a can

29t A P P IS N D I X.

can be no great occafion for b^ng more explicit
It will'iiot, iiowever, be amils to add the foUofwlDg

demonftration. is the prcfcnt probability

that a life whofe complement is n will fail in zoy

4ta

one aflignaWc year of its duration* S X — H — i

+ -^y &c. :(^), or the prefent ralue of i /. per arh

Hum for n^ years^ multiplied by -.« is the pident

value of the fum or legacy denoted by S, paya&
at the failure of the given life. Therefore, (ji be-^
^tig s^ ; the life 30 \ intereft 4 j>er cent^ r^n > •04 »
the fum 25 A) the value of the expedation, by
.Mr. t>e Moivreh hypotheiis, is 9*9 19.

Further. The value of i /. to be received at the
end 6i a year, provided the life whofe complement
is n hiTls, is -the probability of the failure of the
life multiplied by i L dilcounted for a year, or

■wai^

nv^» I W

' I — -— X -. In like manner : die value of i /.

n r

*

HO be received at the end of two years, if the (ame

«*— 2

4i£e fails in 2 years, is i — — — * X ^, Aa4» there-
fore, the value of all the poffibk payments of an
eftatc or annuity of 1 /. ior ever, to be entered

mm ._ . g W

upon after the given life, is i x - '+ i —

% — 2 .1 n — 1 . 1

n

X-+ i -^x -^ &c. (») + —:, +

r'+'

APPENDIX. 293

--Tt, &c. or - + -i + 3, &c. h — p +

2lll?, &c. that is, the value of the life fubtrafted

ironi the perpetuity ; or, in this example, /. 14.684,
(the v^lue of a life at 30) fubtra&ed from, 25 $ chat
is, /. 10.316. But 10.316 is to 9.9 19, in the fame
ratio with 104 to 100, or 26 to 25» agreeably to
the rule in the Scbotium.

^

U g Note

«94 appendix:.

Note (F). Queftion XIII. Page 44.

i

WHEN 1 here call 48 the mean age of all mar*
ried men, and 40 the mean age of marric4
women, I do no( intend to fuppofe, that there are a|
many married perfpns who exceed thefe ages, aa
there are who fall (hort of them* It is likely that th(
latter are moft numerous ^ and it is necefiary that
this (hould be the cafe, to render the fuppofition I
make juft. — If all marriages commenced at 33 for
the man, and 25 for the woman, one half of them
would be diflblved by the time the men were 50^
and the women 42 ; for (by the Hypotbifis^ and
alfo nearly by the jSreflaw^ fforwicby and ^ortbamp^
Un tables) there is an equal chance for the joint
continuance of two lives, whofe pges are 25 and
33, feventeen years. Forty- two and fifty then
would be properly the mean ages at which widow-
hood would commence; meaning by thefe " the
*' ages on each fide of which equal numbers are
** left widows and widowers.'' — i^But, tho* in this
cafe half the marriages of every year would be dif**
folved in 17 years, they would not be 0II diOblved
in twice that time. So far would this be from
happening, that about a 7th part would continue
beyond twice 1 7 years ; nor would it be certain^
fhat they would be all difiblved till near the ex-^
tremity of the pofliblc extent of life, Tho', there-
fore, an equal nuipber of marriages would be dif-
jTolved, or an equal number of widows and wi-
dowers left before 50 and 42, and afterwards^ yet
(he ages of the latter would, one with another,
much more exceed 50 and 42, than the ages of
ilie fprmer (that is, of the widows and widowers left

4 M^r9

APPENDIX. 295

hifori 50 and 42) would fall fhort of them. And the
number of marria^s alfo in the world, among per-
fons of greater ages than thefe, would be much
fewer than among perfons of leflfer ages. — In other
words : the period, at which the marriages that
liave been contra6^ed are half diflblved, is not the
period at which the number of marriages conftantly
exifting is equally divided, but this period falls
fome years fdoner ; and the period I have in view,
falls in that part of the interval between thefe tw6
periods, where the greater ages of the marriages
on one fide, are juft enough to compenfate (in fuch
a calculation as that I have given) their deficien-
cies in number, compared with the number of
marriages od the other fide.

In fhort. Suppole 35 marriages every year,
between perlbns 33 and 25 {a). In 12 years there
Hirouid be half as many in the world, as could
poffibly arife from fuch a number of yearly wed-
dings. In 17 years, half every fct would be ex-
tindt. The expellation of every marriage would b«
1 9 years, by prob. 2 1 of Mr. De Moivre^s Treatife
an Annuities^ or by the note p. 305 : 1 hat is,
taking them all together, they would axift juft as
long as an equal nwmhtr of Jingle perfons, fuppofed
to be fure of living juft ig years, and no more :
or, as long as an equal number of fingle perfons,
^all 48 years of age, fuppofed to be fubjcft to the
commdn laws of mortality. One with another,
then, they will be all extinft in 10 years: the
marriages which continue beyond this term, tho*
fewer in- number, enjoying among them juft as

(a) In the Pais de Vnud^ S-witxerland^ the mean age at which
women jnarrjs is nearly the very age here mentioned : But it
will be (hewn in the Supplemtnt^ that the expe^attoo of mar-
riage there, is no lefs than 23 years and \ ; io much higher are
the probabilxtiesof life in t\itiOUHtry than in townt^ or diaa they
ougnt to be according to Mr. DeMoIvre^sHjfotbefii, See p. z6i,

U 4. much

£96 A P P B N D i X.

much more duratioo, as thofe that fall fliort- of i|
enjoy lefs. ff^idowSj then, ax a medium^ will coo^
lucDce widowhood ar 44(ch^t is, ^5 increaicd by 1 9)
years of age^ and mdowers at 52, The values, tber&^
fore, of the lives oi the former^ when they commencs
widQwhood,wiU,one with aaocher, be the iaoie witi^
the value of a life at 44 ; or, (reckoDing intcreik at
4 per cent.) 12.5 years purchaie, in one prefeoc pay*
tnent, (the annuity to begin at the eiul of a year) |
and their expeSaiion of li^ will be 11 ff^fs, or half
the difference between 44 and 86. The value of
the lives of the latUr will be 10.919 and their «r*
petlation 1 7 years. — The whole nuniber of marriages
conftantly exifting, which would refiilt fcom 35
ibppofed to commence annually, would be 19X351
or 665 \ and 53 years (the difference between 33
j^nd 86) would be (he time in which they would in-
creafe to this number — The chance of furvivorlhip
would be the odds of 69 to 53, by prob. i8tb^
Mr. De Moivre on AnnnUies ; that is, in 53 years^
j5 relidb of thefe marriages would be left every
year, and the number of widows would be to the
number of yiidowersy as 69. to 53 ; or 19.8 wid(m$
tvould be left annually, and i^.a wUowirs. The
pioximum of widows in life together^ if none mar*
ried, v^ould be 21x19*8, or 416; and they
yvould increafe to this number in 1 14 years (or 61
years after the number of marriages had attained

to a maximum) The maximmi ^ widower s^oviA

be 15.2 X 1 7f or 258 \ and they would increafe tQ
this number in 106 years,

An eafy method may be hence deduced of Iblv*

ipg the queftion which occaGons this note If

the nqmber of the members of the eitabliihmenc
1 have fuppofed, is 66^% and the ihean ages a€
which marriage may be deemed to commence are
25 and 33, ig.8 widows will (ithas juft appeared)

be

..J

1»e left ever/ year % «uid iVht valtie& ^ their Ikes^
when fhcy comaien^e widowbood> will: b^j one
i^kb ancxher, i^t ytarf purehafie, hn aimuicy cf
so il willy therefore, be worth, t&each widow, 250A
and I9.& iwrb aRfiuicies muft be worth 4950 i^
whklv CQafeqacrKlyy id the annual iiicome nccef-
fefy for the fupport of the eftablifhnnenc^ the gift
payment to be received unmediatfely : or /. 7.44
frgm each of the 66^ members \ whkb aofwees
nearly to the deGerinuiatioii ia the note page 44.

lathe laft Eflfay, p. 275) ^^ ^^ ^^^^ (hewn^ that
obfervations deterfnine the cbafKe el forvivorfltip
jjo favour of the wife ki marriage, fa be realljr fo great
^ 3 ta 2 ; and? in focne €ircuir:i]:aAee9 greater. I have
alfo there ob&rved, that in order to account f(^ thi%
from the difference of age between men and their
wives, this difference nwd be at leaft 12 years, and
the mean agiea of alt who marry annually, muft be
fcppofed to be about 23 and 35. In this cafe^ 1%
as before, will nearly be the expeSaiion of all mar«-
riages. The mean age at which widows and wi-
dowers will commence fuch will be 42 and 54. The
Aomber of annual marriages neceflar y to keep tip
^5 marriages conftantly exilling, will be 3^
The number of widows left annually, by fuch a
number of marriages, will be 21 \ and the values
of their lives, at the time they commence widow*
hood, will be 1 2.85 years purchafe by Table VI : and
therefore, the whole anni^ income neceffary for the
fopport of the fuppofed eftabli(hment,will be 539:* #•
or an annual payment, beginning immediately, of
/.8. 1 1 from each member-p-The number (rfwidow*
on fuch as eftablifhne^nt will, in ^3 years, groW) if
none marry^ to 462 ; and the number of wicSoweri
to 224.— —It n\ay be depended on, that all this
would happen as far as Dr. Hallefs Table, or the
Tables for Norwich and Nortbamflony exhibit the
true ftate of human mortality,

Anwng

\

1

49^ APPENDIX.

Among the miniftcrs and profeflbrs in Scot*
l»AND, the number of married men being 66y^ or
nearly that here mentioned, the number of annual
weddings has, for many years, been at an average 31,
and the number of widows left annually 19.2 ; andt
therefore, the chance of furvivorlhip in favour c(f
the wife, as 19.2 to 1 1.8, or 5 to 3. See Eflay I^.

f. 274. This is not more different from the refults
have given, than might have been expedled ^
and the chief reafon of the difference is, that -the
ixpeSations of Jingle and joint lives among the mi-
nifters and their wives in ScOTirAtf d, are greater
than thofe given by Dr.flatley\ and the other ta«

bles of obfcrvation- ^Thefe tables give the ex-

pe£tations of lives as they are among the bulk of
mankind in moderate towns. The expedations
of lives among the better fort of men, living
tnoftly in country villages and parifhes, are much
greater. The h& is, that among !;he minifters in
SiotUmd^ the expedation of zfingU life,, at the age
of 27, is three years and an half greater; and,
o( joint lives, about two years and a half greater,
than the fame expectations by Dr. Hatlefs Tabl*.
Ibid, page 269.

I cannot help juft mentioning another remark
here.— —It may be obferved, that fuppOfing nd
fecond marriages, and, at the fame time, that th*
odds for the woman's furviving in marriage is 3 to
2, the number of widows in the world would be
dcuile the number of widowers. But it has been
found, in fadt, that the number of widows is five
times the number of widowers. How this is to be
accounted for, I have (hewn in the £fiay juft re^
fcrred to, page 276.

Note

A PP END rx. 2^9

Note (G). ; Qucftion XIV. Page 48.

LET r be i/. increafed by its intercft for one
yeaf i t the given time or number of years
tor which the alTuranc^ is to be made ; a^ 5, r, &c.
the fr/>babilUies takeft out of a table of obferva-
jtions, that the perfon whole age is given (hall live
l> 2, 3, S^c, years ^ and P the probability that be

fliall live / yeaVs, Then i^ + ~^ 4- iZIf , &c.

!;, &c. (/) -f + i + ^, &c. (/-,) + ^ +
i^^ X - + -» -f -; J &c* w»U be the exaft value

ft r r* r^

q{ an annuity to be entered upon at the failure of
the given life, provided it happens in / years,
And the rule is nothing but this value cxprel]^
in words. In a (imilar manner may be demon-
ftrated the other rule for finding the values of
aflurances for a given time, mi two joint lires^ or
the loagell of two fives.

Note

300 APPENDIX

Note (H). Qijcftion XV. Page 56.

LET r fignify as before; S the given fum to
L be afiured ; / ihc given time *, N and n tbe
number of the living in the table of obfervations,
at the age of A and B rcfpeftively ; A, B, C, &c.
and tf, kj €j &c. the number of the living in the
table, at the end of i, 2, 3, &c years from the ages
ofAandB; &» D» D, D, &c. and 4» d^ d^ d^ &c

in in \ It HI

the decrements of life in the table, at the end of
I, ^t 3, &C. years nom the fame ages. Then, by
reaibning in the fame manner with Mr. Simpfon^ in
p. 3 1 6, &c. SeleS Exereifes, it will appear that S X

Axrf hud C*d Dd

~D5 157" s Ad B3

C7" S Ud D7

|3~.&c. ii)-^-^X -+;^.&e. (/). This

IS the exaft anfwer to Queftion XV. and the rule
is as near an approxiniacioo to it as there is reafon
to defire, .

In the fame manner, retaining all the fame fym*
bols, it may be found, that the anfwer to Queftion
XVI. is

Dd Dd U+DXd D+D+D^d

Dd Dd Hrf I

^ ". aN»r* ' aN«r' aNwr*

A P P'E N D I X,

S***

S D</ . Dd

&C. (/-O + JFJ X .^ +. Xi ^ ni, &C (/J.-

D D+D D+D+D ^ , > . ,

fMae wkh the ^xcefs <^ the valtie of an annuatf
pertain for a number of years kfs by one year than
the given term, above the vilue of an annuity on
the life of A, for the fame number of years ^ from
whence the reafon of the rule lor £)lving this
^|ue(iion may be eafily difcovered.

Note

|09 A P P E if'I^ 1 X.

Note (I). Page n8, &c.

« «

LE T / be any given term of years { p tlic viP
lue of 1 /. due at the end of the given term';
A the vaki^ of an annuity .certain for the fame
term ; n the compUmeni of a given life; G the va*
lue for the given terniy of two joint lives, both
equal to the given life ; (to be found' by Qwcft. VI.)
P the perpetuity \ r, i /. increaled by its intereft for
one yea r.

Then A— G X /^ +/ k/><P— A X P X r will bfr
the prefent value of i A a /. 3 /• &c. (/) payable at
the end of 1,2, ^, &:c. (/) years \ but fubjeft to
failure when the given life fails*

If fuch a courfe of payment is to begin im-
mediately, and to be made at the beginning of
every year, till / + i payments are made m t years 5
add to the preceding value, the value increafed by
unity of an annuity on the given life for / yearr,
found by.Queftion VI. and the yi/m will be the va-
lue fought. And this value divided by the pre-
fent value of what may happen to remain of the
given life after / years, found by Queftion VL will
give the Jlamling annuity to which luch a leries of
increafing annual payments, beginning immedi-
ately, will entitles for the remainder of the given
life after / years.

With the afliftance of this theorem, all that is
faid in p. 117, &c. may be invciligated. It
would be too tedious to enter into a more minute
account^

Note

APPENDIX. 303

Note (K). 'Page 149.

LET rf fignify the Jiffermte between the em-
, plnunts of the youngeft and oldeft life in
the body of Annuitants, here defcribed, at the
time they enter j let S fignify the fum of thcfc
^empUmiHtSi n any given number of years not

greater than -—- -» and x the ratio of the whole

number of Annuitants to -— - . Then

My(,i will be the number that wUl die the ift year >

jf^4j^j£^ the number that wiU die the 2d year j

*X^+^ + §; + gi. 4th year,

8^ lid ibd , ltd ,

*X^ + T+^ + Tr+ c^^ 5th year;

"s ^ s* ^ s» ' s

d %d

and ;f X^^'+ff'— »X Q +»— a +«— II* X r; +»— 3

&/

ivai be the whole number dying in n years. When

S d

n is greater than , this fcries is greater than

the whole number dying in n years ; but in all
other cafes it gives this number exadly, fuppofing

the probabilities of life to dccrcafe uniformly.

In

^4-

App eu Dix:

In the prefent inftance, the youngeft life being 3d,
and the oldcft 60, the two CQtnpkaients are 56 and

&f

±6. S =i 82. </ = 30. -- — 1 230. And therefore xzi

mm

^|~ —zjai, Take « = 30 jiears, and the forei

h ■^■<<>il

^bg ferics wiUl^e 27. J X 900^ 318.2 + 7.^142 +

whole number dying in 30 years, bujc at the fame
tisM k&thsHi fliie wbcfte numbtfr cf AnmiiiatKs.

I :

Now

Ai>l?END^i±. 30J

- • • . ....... ^ '

Note (L). . Sec Effay I. Page .170, 171,

173- • ■-

l*T^Hfi fum 6f tfifc prtfbabinties tKat any giveh

X . lives will attain to the end of the i ft, 2<J,

gdy, Sec. years frorn ihe prefcnt time to thejjtmolt

extremity of life (for inftance, ^4 4- -J4 + try &c.

- to -Tff =22 4 for lives of 40^ by the byp.otbcfis) may
be called their expeUafiotiy or the number of pay-

. (iteitts due to them^ ^% yearly anmitants.i T^he fum
of the probabilities that they will attain to the end
of the lit; 2d, gd* &c. .i?a^jF^^i,'(e^, in theparti-
culat cafe fpccififcd^ ^^^^^^^ 4{., &Cj =

' V hif^ yti^i^ or 22>| ytan) is their expedition as
half yearly annuiiants. And the fums juft men-

' tJonc^ of the t5r6bafbihties of th«ir attaimng to the
end of the ift, 2d, 3d, &c. moments (equal in the
Ijtfne.paf^tcqlar cafe to 23 years) 'is properly ^thqir
expeHatian of lifey or their expeSatioh as annuitants
iecurcAby land. ..J..-:\ ; ,;

Mr. De Moivre has omitted the demonftrationd
df ^i!Ke rules he ha$ given for finding thcexpltSa^

'tions oi lives, ajnd only intimated in general, that
he difcovered tBcm by a calculation dc»cfuced from
tte mcfdiod of fiuxioi^St See his T^TtatiJt on Annuu
ties^ page 66. It will, perhaps, be agreeable to
fdme to fee bow e^fily they 3t« dfcdoced in this
method, upon thp hypothef^ of an equal decre-
ment of life.
ljet;rftand for a moment of time, and n the

cp9^lement of any alfighed .life. Then -^^ —— i

i'-^-^^, &c. Will be tlie prefent probabiliric$ of its

X con-

3o6 A !» P E N f) 1 it.

continuing tb the end of the ift, sd, 3d, See. tath

ments ; and — — the probability of its continuing

to the end of a; time. x i will therefof^ be

the fluxion of the fum of the probabilities, or of an
ar<a reprefenting this fum, whofe ordinaUs are

— , and axis y.— The/wn/ of this expreffion, or

y — — , is the fum itfclf for the time x ; and this,

• "when x=i)i,, becomes 4^,'and:givie$ xhfi.esfpejffaiipn of

^ihe affigned life, or the ^ax ofall cbe^pm^i^Uip^

juft mentioned, for its whole poflible dwatiQiu-^In

viike maoaer: fince T^, la the probability that

■i ^

•r

two equaljbint lives will continue AT time, !!!lIfL X*

• ' ... ^ , ^.

will be the flaxtM of the fum of the pfobabilities.
ThtflucfU is* ~ J +^» which,.w,hcn/f=x,is,-,
or the expcQiatlon of tw6 cqud jomtiives.-*— —

Again : fince X — is tht probabittty that there

will be a furvivor of two equal joint lives at
the end of x time, X — X * will be

n n . .

the //ifx/^ of the fum of the probabilities ;

' and thefluentydr — — — ; is (when x±in) in, or

xhi^£9f>^a^^ef (ucvivorfliip between ^wO eqtial
lives ; which, therefore, appears to be equal to the

I

. iion of (^o^ HHipuU joint Ufcs, found in the ^

!wray, is > T-- r- , » being the cbff^lmetff o£ tl^
oldeft life, and n the cmpUmeni of the youhgcfti

'The whole expedbtion of funrirorihip ir - -^ ^^^-f^

»

1^. . And the. expcaatiQfl pf. furviyot^ip of. the
oldeft.will bfe to the expeftation of funriTorihip «f

r ofjthe yoongcft, ^'^ 6^ *** a ^ a "*" 6a' ' ^ *' **^

. tti 4ppI]F this ~ wvJ^S^pmn ta any Aaint>er. of joutf
4irtics,,«H4WaU4«U^offtjrv4vo«flup. ^

; U-tftif be o^rycd, coacerniog_th<; firft of tb^

^fluents hcr^ giwcn, that J't expr^cs no^ oriljr. the

;ez{K^tif>n of- s^' fpY^n-, Ijfe . for . the tigje, «,^ j»/)d

;t|»eB|fqre its cWhj>lc expe^atioo w^n, «=», bpfi

liJwwiiei. the^ nijii^r of peribns aTiire, to ^hich o^e

-.p«rf95^.ad4ed.aq»iaUK..to a/odety^aij a giy^ ^jge^

^Jtfci the^fore,-.i? 58,, o? «^^/>» of Ufe. ?^)
jt9<?oipe Mpoo a i<!?i?t)t wcry .year j, : the lUJWJCtpf
<*iWeifiiOts .alwe,. «ifd»Wd' ftjont hence,,, will,, ii];,«r

drears. be«.-r j^, ""'^-^^^ ''^ and.there-

■forej thci number T)f annuitjujts alire, .deduced^ in
,;ihclame4?ie,;^tnji.^PRuit^9ts, kft a^nu^y^^at

the fameage^ will bc^^^^X^* ^InJike

#m9n?r,..thF,a4J««»t.. ^^^^'^"^ ? *t *j g»/«? *«

X a number

3o8 APPENDIX.

number of marriages in being together, that w9f,
in X years, grow out of one yearly marriage, be-
, tween pcrfons of equal ages, whofc complement of
'life is n. If they are of unequal ages, and the com-
plement of the oldtft life is nr, and of the yoongep:

ir, this number will be -^ — ^ 1- x. And

' . yim %nm

Jii the number of years is required, in which any
"given number of yearly marriages, between men
. and women at given ages, will increafe fo far as

CO be in any given proportion to the greateff num-
'ber that can pdflibly grow out of fuch marriages,
^this expreflion mud be made equal to the expeHa--
'Sidn o( the joint lives,' or of each marriage, mukt-

plied by the fraftion expreffing the given propor-
'tion ; and the root of the equation will be the an-
:fv^er. Thus : it may be found, that one marriage
""every yeat, between perfons gj and 25 years of
'age, would in xo years increafe to 8.35; 'in 15
^years, to 11.38 ; and in 53 years, to 19, or their

greateft poffible number; and, confequently, that
^35 fuch yearly marriages would, in 10 years, in-
'creafe to 292 ; in 15 years, to 398 ; and in 53 years,

to 66§. And if it is enquired in what number

^of years 35 fuch yearly marriages would increafe
^to half the number in being together, poflible to
. be derived from them, the value of ^, in the cubic

.equation — ;;jj^ + X = - - g-^ Xi. muft

'.be found; which, in the prefent inftance, is nearly

-12U

I have, in fome parts of this work, had occalion
JLO make fuch dedudtions as thefe. See note (A),
p. 283 ; and note (F), p. 294; and Queftions III.
•and XIII. . .

Note

APPENDIX. 309

Note (M). Eflay II. Page 23 1 .

LET r fignify i/. increafed by its xntcrcft for
one year.

V the PERPETUITY.

n the difference between the age of the youngeft
life, and 86 ^ or its cmplemet^t.
. m the compleiTient or the oldeft life.

P the value (in Table II.) of an annuity certain
for m years.

And the exatft value of any two given joint lives,
according to the hypothelis of an equal decrenienc

v+i mzzzzzzzz P

of life, will beV — - xn — m—^zv — i X Z

W- »Vi^ Example ;

Let the ages b^ 27 and 38 ; apd the rate of in-
tereft 4 per cent. Then » =: 59. m = 48 . V= 25.

P = 21.195. «-*-iiii— 2v — 1 = — 40. n — wr—
p

2t;_ix-+2'^=^5P-^' 7-660 = 32.340. And

V4.T P

— ^X»— »— 2V— ix-+*v=*5— 44

X 32.340= 10.748, the value of two joint lives
whofe ages are 27 and j8.

X 3 Note

r

.i

^10 A P J^ E- If D I' X;

Note (N). feffay ttl. tag6 237,

IT is plain that the purchafer qf A^s* rigfit^* ^
ftatcd in the firfl; of the quetf i6rts, to Which this
note refers, cannot get into pbflcljion, tiff the y*af
when A ^nd B (hall be both dead ; hbr the«, tnt-
lefs A happens to die laj. Now, (tipp6fing the
comrhod coniplement of life i ; the {ifotjabifity
that A and B (hall he both dead at the end of thd

jirj yea', aHd A dit laft, iM — ?^ it i

t I ♦ « > •»

^ 1 = l-.?=£_?±i +f::^._-.i„ like

2 2 2)» 2» 2Jf*

nianner, the probability that they (hlU bd ^^/ft
dead at the eiid of the 2di 3d; &fc, yliariJi add A

. ,1 ;r — 2 » — 2 . w— 2*^ I

furVlVC, IS*. — ~^ — r— TT-f ■ 3 J S T--

2 2« 2« 2^ 1J 2«

^?^ + ^^~^ , &c. The prefint value, thfcJ^or*,
of the I ft, 2d, ^d, &c. renti; of the rcvferfionarf

eftateis-- r^ -r- — t- , r-=— *r

2r 2^r 2w ifrr ' 2r* 2ar*

» — 2 , «— 2V I n — % n-^% , «— 5\* 4,

_ O- , — — I '^ — —^ 4. ■ '^■■. &c.

2»r* 2»V* 2r^ 2«r* 2«r»' ' 2»*r*

Suppofing r to (ignify 1/. increafed by its intereft
for a year % and the cftate to be i/. per annum. And
theyi^ffli of thefe terms continued in infimtum^ is the

value requirel—^But i + i 4, i, &c. is ta^

the

A??E.15PI,X. jii

the perpetuity. And ^;p + -;;^ - -^^

jtm- a«r* 2«V* ^ aiir« ^ aw* a«*rJ *

is half the value of thej^ni lives, fubtraffcedfrom
batfxJtkt futn of the values of the tvto JingU lives ;
that is» half the value of the hmgefi of the two
lives,

A fimilar demonftration may be applied to the
other queftion.

X 4 Note

312 APPENDIX,

Note 46). Effay ^V. Page 267. -

LE'T r be I /. increafcd hf its intcrcft for on^
year.
" Let S Tcprdcnt any given interval of time, or
number of years, during which the decrements of
life in a table of obfervarions continue equal.

a the number of the jiving in the table at the
beginning of the firft year of that interval.

i the number of the living in the table at the
beginning of the year immediately following the
^me interval.

P the value of an annuity certain for S years.

p the value, in Table I. of i /. due at the end
pf S years.

Q^the value, in Table VI, of an annuity for the
life of a perfon whofe age wants S years of 86.

N thp yalue^ in ftrift agreement with the given
table of obfervations, of an annuity on the life of
a perfon whofe age is S years greater than the age
at which the interval of equal decrements begins.
Then,

<5L+ - X P — Q^will be the value, according

to the table of obfervations, of an annuity for S
years, on a life pf the, fame age with that at which
the interval of equal decrements begins. And

Q^+-X p Q+ p^ will the value of an

annuity on the whole duration of that life.

When S reprcfents one year ^ Qvanifhes, and the

Jaft cxprcflion becomes — X 7+N > which is the

rule

APPENDIX. ^i^

role for finding^- from the valpe given of any life;
the value of a. life ope year younger.

Thcfe Theorems favc much labour in calculat-
ing the values of life-annuities from tables of ob-
fervations.

The firft of them, with its inveftigation, may
be found in page 1^41, 3d edition, of Mr. £V
'Moivr^s Trtatife on the Doifrinc of Chances. But it
is neceflary to obferve, that the diredion Mr. Di
'Maivre has given for finding the value of Q^ is
wrong. In confequence of calculating agreeably to
this dire£lion, he gives the value of a life at the age
of 42, by Dr.HaU^^s table, greater than the value
4>f the iame Ufe by his own hypotfaefis ; whereas, it
is evident, that the probabilities of living after 42^ "
l^dng all along leis in Dr. HaJley^s rable» than in the
hypothefis, the value of the life muft be aUb le&

The mathematical reader may eafily fatisfy him-
felf, that the value of Q ought to be taken from
Table VI. as I have direfted.

An eafy and accurate method of finding the
yalues of fingle lives, agreeably to any given table
of obfervations, is given by Mr. Doafon in his
Mathematical Repcfitory^ vol. II. page 161 •

There is alfo in Mr. Simpfoiis Seleil Exercifes^
page 275, a very eafy rule for approximating to
the values of fingle lives, according to Dr. Halleft
table. But this rule muft not be depended on ;
for I have found it half a year's purchafe, and fome*
times three-quarters of a year's purchafe wrong.

To prevent the danger of miftaking the Theo-
rem I have given, I have thought proper to fub-
join the following example.

Let the table of obfervations be the Brejlatv Ta»

ble^ Of Table IIL The value of a life at 70, by this

/ Table,

JI4 A P P E N. D I. X.

Table. is^+ eg; + ^» &c. to the end of

life. The number of terms in this feries beins
ihmlU it n^y bq eaGly found tq bq 3.514, fuppoH

ing intcrcft a? 4 /^ r^»/. and ^^ -p, — , &c. fac-

ing the values^ in Table L of iL at the end of

tj 2, 3, &c. years. ^Frpm 78. to 74 the decrc-

loents of life concinue ^ual \ aod cberefore $=4.
4=98, 4== 58. P = 3.6x98, by Table H; ^ =
•8548, by Table i ; 0= 1.406, by Tabk VI 1

N = 3.514- P-^Q^+/N=: 5.227; and<:^+-»

XP — Q^-f/N = 4.50Q, or the v^lttc of a life at

74-

* From 74 to 70 there is another interval of equal

decrements ; and, by a like eafy operation, thfe

y#lge of a \if^ at 70 will be found to be 5.595*

TABLE

T A B I, E L

^»t

Tbe-pi^cnt Value o£ lL to be received at the end
of any number oS years, aoi exceeding 100&
fjifcountiog ac the rates of 3, 3^9 4> 44> 5 ^9
6/^ r<«/. coffipoand intereft*

-mi^^^r^^mf

jptra.

■■ 11 1 . I ■

I ,970874

a ,943596

4 ,888487
$ ,862609

6 .837484

7 ,813092
81.789409

,766417

•744^4

9
10

«

II
it

i4

id

zo

31

22

«4

xS

'9

30

3«
1*

•722421

,701380

•08095 1

,661118

•641862

,623167

,605016

•570286
• 553676

,966184

t9«5«»
•901943

•871442

»84>973
•813501

•785^^1

»7594"*

»73373»
,708919

,684946

• 661783
,639404
.617782

• 596891

• 576706

»5S7«04

•538361
t5SOi$6

,502566

4P»rCt.

^im

,961538

i9H556
,888996

»8548o4
,821927

1790315
,759918
,730690
•702587

•675564

4iptrCt.l SperCt.

6p«ret.

.956938 t95 2381
♦91573^*907029
^876297 ,863838

■^■v

•537S«
•521893

^506692

•491934
•477606

•463695
•4501^9
•437077
4*4346
•411987

•399987
•388337

.649581

.624597
,600574

*577475
•555*65
•533908

•5*3373
•493628

•47464*
•456587

.838561
•802451
,767896
,734828
.703185
,67290!
•643928

•616199
•589664
• 564272

.539973
,516720

.494469
•473176
,452800

H3330*
•414643

•485571

•469151

•453«86

•437957

•4*3147

^^08838

.395012
•381654

•368748
•156*78

344*30
,332590

.4388^4

•4**95-5
,405726

,390121

.375H7
,360689

,346817

•333477
•32065 1

.308319

,296460

,28505^

.396787
.379701
•363350
•347703

•33*731
•318402
,304691

.*9'57i
•279015

•267000

•*5550*
,244500

,822702
•783526

,746215
»7io68|

•676839
,644609
•613913

,584679

•556837

•530351
,505068

481017
.458112
,436297

.41 552 J

.395734
•376889

.943396

,8^996

,839619

• 792094
•747258
,704961

.665057
,627^12
,591898

.558395

K ■

.35894*
^341850

.32557*
,310068

•295303
•281241

•267848

•255094
• 242946

.231377

,$26788
4496969

.468I39
•442301

•4*7;6|

.393646

.371364

•3508441

.330513;
.311605]

»«94^S5!
^*77$oc

•261797I

.2469791

.252999

.*i9*i5j

,207.36a
,195630
•"845571
.1741 1«»

,220359

,209866

•164*551

^i6 A R P E ]^

T A B'L E I. CoBlinucd.

jferpt.

33 »377026

34 .36604^

35 J3S5383

36 .345032

3r •334983

38 ,325326

39 »3«5754

40 .3065 57

3jperCt,

•52' 343
> J >P476.
i299977 .2534«5

4 p£r Ct.

»*74094
»«63552

4«

4^

43

44

45

46

47
48

49

5©

5'

53
54

S7
58

1^

,297628
,288959
,280543

>«7«37a
,264439

•256737
,249259

.241999

,234950

,228107

,289833
,28003 a
.270562
,261413
,252572

,221463
.215013
,208750
,202670
> 196767
,191036
1I85472
,180070
,174825

•■09733

•■

61 ,164789

62 ii5999<'

63 •"553iO

64 ,150806

65 ,146413

66 ,142149

67 ,138009

68 ,133989
6g ,130086

1 701.12629^

,244031

•235779
,227806

,22Ot02
,212659
,205468
,198520
,191806
,185320

•'79053

,172998
,167148
,161496
,156035
.150758
,145660
,140734

•'35975

•«3»377
,126934

,243669
,234297
,225285
,216621
,208289

,200278

.'92575
,18^168

•178046

,171198

,164614

,•58283

.152195
,146341

.1407 '3

4}perCt.

•23397'
,223896

•2 '4254
,2050/8

,196199

,187750
,179665
f 17 1929

.164525

,157440
,150663

»'44<73
»« 37964

»«32023

,126338
,120898
,115692
,110710

.5 per Ct.

,199873

••90355
,181290

»'72657
,164436

,156605

,149148

,142046

1 122642
, 1 1 8495
,114487
,110616
,106,875
,103261
,099769
,096395
,093136
.019986

,135301

, 1 30097
,125093
,120282
,115656
,111207
,106930
,102817
,098963
,095060

,091404

,087889
,084508
,081258

•078' 33
,075128

,072238

,069460

,066788

,105942

,101380
,097014
,092837
,088839
,085013
,081353
,077849

•074497
,071289

,135282
,128840
,122704
,116864

,111297
,105997

,100949

,096142

,091564

,087204

,08305 1

,079096

>07533o

•07*743
,068326

,065073

,061974

,059023

,056212

•053536

6 per Ct(

,146186
f'379»2
,130195
,122741

»"5793
,109239

,103056

,097222

,091719
,086527
•081630
,077009
,072650
,068538

♦064658
,060998
,057546
,054228

,068219
,065281
,06 24:^0
,059780
,057206

•054742
,052385

,050129
.04797 «

,0642191,045905

,050986
,048558
,046246
,044044
,041946
,039949
,038047
,036235
,034509
,032866

,051215

,048316

,045582

,043001

,040567

,038271

,036105

,034061

•032133
,030310

,028598

,026989
•025453
,02401 2
,022653
,021370
,020161
,019020
,017943
,016927

- I ■ ■

N D J X.

3*7

TABLE I. Continued.

<

7»
72

73

74

76

7.7

78

79
80

82

86

87
88

3 per Ct.

22619

19047
15580

12214

08945

05772
02091

;099700

,096796

t093977

,091240
,088582
,086002

,08^97
^081065

,078704

,076412

,074186

891,0^2027

90

,069928

91. ,^67891

92 ,065914

93 ,063994

94 ,062130

95 ,060320

96 ,058563

97 ,056858
981,055202

99^o53594
100^092033

,086943
,084003
,081162
,078418
,075766
,073204
,070728
,068336
,066026
,065793

,061636

>0595J«

»057538
,051592

»05J7»2
,05r8g6

,056141
,048445

,046807
,0452^4

4perCt.

,061749

>059374
,057091

,054895

,052784

>^50754
,048801

,046924

,045120

,043384

,043695
,042217
,0407851

»0394^<*

,038077

,036790
^035546

^034344
,033181

,032060

,041716
,040111
,038569
,0^7085

t03S^59
,034287

,032968

,031790

>03O48 1

,029309

,028182
,0270^8
,026055
,025053
,024090
,023103
,022272
,021416
,020^92
,019800

4JperCt.

,043928
,042037
,040226
,038494
,036836
,035250

•033732
,032280

,030890

>oa9S59

,028^8?
,027068
,025903
,024787

,023720
,022699
,021721
«02o786
^01989^
»0i9d34

,018215
>oi743b
,016680
,015961

,015274
,014616

,013987

,013385

,012808

»o»az57

5 per Ct*

,031301
,0298 1 1
,018391'
,027039

,t)25752
,024525
»0233S7

,02324{
,021186
,026177

,019216

^0183011

,0174^

1OI66OO

1OI58O9

,015056

,014339

,013657

,013096

»oi,2387

,011797
,01123^
,010700
,010191

,009705
,009243
,008803
,008384
,007985
,007604

6,pcf Ct.

015^9
015065
01i|^12
013408

or2txj9
011935
01125^

0|062CJ

OIOOI9

00945a

00891;^
008412
0079^

007487

007063
006661
006286
oos93<>

OQ559I

005278

004979
004697
00443 i
004181

003944
003721

oo35>9
0033U
003 1 24
002057

T A P L E

T A B LJE II.

iTbeprcfcnt Value ofaft Annuity ofOncPoiiildi
, ] -foragyNuinber6fryearsnotex€ec3in^ro<jf
i ^Vtht fetrcral 'Ratesr of 3, ji, :4i ;5, -aikl- 6/*
iferCent.

\

I

f

.&

■ 6

I

9
r'ib

1

:• 1;

3 pe^ Ct. I

^4 5797

5497 »

f 7.0 J 96
.7.7864

N.jr3«2

ji per et

I > 1

♦9662
»;8997

II
12

14'.

»'i6

»7
I. 1.8

19

20

-•■ >"-- ■

■ g.252i5

' 9-954P

li.y96b'
iK9379

21

22

24
25

12.561*

*3.r66T

14-3238
14.8774

'5^3a46

'^.»<45
'6:8746

7i6o77

8(.39i^

9,00.15

10:3627
10.92O5

11.5.174

4 per Ct. I $ pef Ct.

.96115
Ii.»8^3
4.7756

I

' 6;00» 3
^.73417

^•4358

a.ti

•9523
2^7232

3^5459
•4j8?94

^ '

i^h*i**BMt«i^'« -mm^

15-4150
15.9389

12.0941

13.1A97
13.7098
14.2124

ir.76
9^9*Sl5

.r5i0.7s6

,5.?863
6.4632

. 7-*P75
7,7firia

6 per Gt

ai^73
.34.65

-4'2X|2

^Ni^

14.6980
I5167I

16.4436 15.6204

16.0584

"».3t36-4
•■^.8632

-9^89816
10.3795

4.9«7
[.582

•2(^

^8(p!l

11.16523 16.8377.

7;-8«€8

48?^38

«.8^6

^■912^9

: 9-7«a

1 2iVSg6
»2ifi59i

i3-»339
13-5903

j.o;iy]^8

ai.«;>4P.M^4{K72

1 4.45 1 1
14.8568
15.2469

16.48 1 5I1 5.6220

6^
12.0853
12:4622

14.0291 12.8211

13.1630

13-4885
13.7986

11.1581
11.4699

11.7640
12.0415
12.3033
12.5503

14.0939} 12.783a

APP'EN'DiiC. ^19

TABLE It. Ciihtibued.

Ye.

"26

zS

■391

:3i

:33
34

I

36

3>

3^

4?

3 per Ct;_

<

17.8768

18.3270

18.7641

19,1^84

19.6004

5f j»erCt.

16.8904

I7;a8^4
J 7l667«)
1 810358
181^920

20.0064
20.3887
20.7657
21.1318

2l'.487b !

42

43
4^

45

4«

471
48

5»

52

53

54
■55

^1.8324
22.1674"
22.4924

22.8o8i

21^.102$

23.h4yl2r.3551

23.412^

23.70^^
23.98^^

24-^.54?
24.5^^8^;^

24.775^
25.^247

5.2667

49 25^5016
59 25-7257

25.9512

20.1662
26.3749
26.5776
26.7744

1 9:0689"

1^.3902

19.7007
20.0007'

201.2905

20.5705-

20.6411

2

i 1.^349
22.0627

22.i828

^21.4955

2^.7009

22.'&$94

23.0912
23.2766

^i'^^56

iz 3.6286

2 J. 7958

•2|.9573
24-^iJ3

' 4 per Ct;

15:9827
16.3295

i6.66jo
16.9837
17.2920

17.5884-
i7;873^

13-9^9^
14.684P

18.147^ 1^.062 k i4.2;^o2

14.368*1

i4-498a

18.4111
18.6646

18.9082
19.1425
19.3678
19.5844

^97927

10.9930
20.1^56
20.3707

20.720Q

20.8846
2 1 .0429
2M951

2i.4^2>I

2 1. 6174 18.3389
18/4180

i?-5^5i
24.2641 122. io36| 1 8.6^ ?4

1-7475
2i.Syi6

2t 9929

jRcrCt.

' 4^375 1
14^6430

I4«8^8<
1 5i 141*0

15-3:724

»5r'5928-
15,8626

16.3741

1^.5468
1 6. 7 IT 2

ii^.86>8
17.0170
171.1590

17.2943
i;l.4232

. , :^-5459
20.5481^ 17.6627

17.7740

17.8800
17.9810
18.0771
18.1687
1I2559

tfferCt.

ite

13.0631

i3-2»o5
i3;406i

i 3^59^7
13.7648

^m

14.62019

14-^460
14.^490
1 5.64612

i^.i38Jo
15.2245

15.3061
i^.38311

»5-"455f8

1 5-5*43
15.58910

15.6500

^5-7^75
15.7618

1^.81^0
15-86^3
15.9069

''$9499

I ♦ ^ m

i»d

A'P P E ¥ Dtt,

TABLE IL Cdtitihatfd.*

V«!.j3perCt.

56

52
58

59
66

•

61
62

65

66
67
68

69
if

7-2

7.3

I 74.

75

76

77
78

79
80

26.9654
27.1509
27.3310
27.5058
27.6755

27.8403
iS'.ooog
28.1556
28.3064
28.4528

28.5950
28.7330
28.8670
28.9971
29.1234

29.2460

29-3650
29.4806

29.5928

29.7018

29.8076
29.9102
30.0099
30.1067
30.2007

24:4097

24.5504
24.6864

24.8178
24.9447

81
82

83

84

85

30.2920

30-3805
30.4665

305500
30.6311

25.0674

25.1859

125.3004

45.41 10

25-5^78

25.6211
25.7209
25.8173
25.9104
26^x304

26,0872
2.6.1713
2,6,2525
26.3309
26.4067

26.4799
26,5506
26.6190
26,6850
267488

26.8104
26.8700
26,9275
26.9831
27.0368

4 per Ct.

22.2198
22,3267
22,4295

22.52*84
22.6234

22.7148
22.8027
22.8872
22.9685
23,0466

23.J218

X3.I940
23.2635
23.3302

23-3945

23.4562

^3-57^7
23.6276

23.6804

23.7311
23.7799
23.8268
23.8720

23-957^
23.9972

24.0357

24.0728

24.1085

5 per ^t. 16 per Ct.

8.6985
^•7605
8.8195

8-6757
8.9292

8.9802
9.0288
9.6750
9.II91
9.1616

9.2010
9.2390

9-2753
9.309.8

9.3426

9-3739
9-4037
9-4321

9-4592
9.4849

9-5094
9-5328
9-5550
9.5762

9.5964,

9.6156

9-6339
9.6514

9.6680

9.6838

6,0288
6.0649
5.0989
&.0311
6.1614

6.1906
6.2170
6.2424
6.2664
.6.2891

6.3104
6.3306
5.3496
6.3676

6.384^

6.4005

^•4155
6.4297

6.4431

6.4558

6.4677
6.4796
6.4896
6.4996
6.5091

6.5180
6.5264

6.5343
6.5418

6.5489

APPENDIX.

311

TABLE 11. Contiriued.

«*— »

.t '.t .lb

87

88

89
90

^^

9»
92

•93
94

9£

i«>«

96

97
98

99
100

•uity.

3 p«r Cc.

30.7098
go.7862
30.8604
30.9324
3 1.0024.

3
3
3
3
3

3
3
3
3
3

.0703
.1362

.2002
.2623
.3226

3822
.4380

•4932
.5468

•5989

34^p«rCt.

27.0887
27.1388
27.1873
27.2341

27'2793

27.3230
27.3652
2 7.4060

27-4454
27.4835

27.5203

37-5558

27.5902

27.6234

27-6554

4 per Cr.

24.1428

1 24.1757
24.2074

24.2379

24.2672

5 per Ct.

24.2954
24*3225
24.3486

24-3736

24-3977

24.4209

24-4431
24.4646

24.4852

24.5050

9.6988

9-7132
9.7268

9-7398
9.7522

9.7640

97752

97859
9.7961

9.8058

9.8151
9.8239

98323
9.8403

9- 8479

6 per Ct.

6.5618
6.5678

6^5734
6.5786

6.5836

6.5883
6.5928
6.5969
6.6009

6.6046
6.6081
6.61 14
6.6145
6.6175

33-3333 |28.57i4h5-oooof20.ooooj

6.6666

TABLE

322 A P P E N D I Xv

TABLE IIL

Shewing the Fjobabilities of the Duration of
Life, as deduced by Dr. Ha fky from Obferva-
tions on the Bills of Mortality of Bresl a;w.

A%ti'
I

Pcrlont
living.

1000

Deer.

of Life.

145

Agei.

3'

Perfons Deer.
living, of Life.

1

Ages,

61

Peribos De<r.
living. Df Ufe.

232 10

523

8

2

S55

57

32

515

8

62

^ 1

222

10

■ 3

798

38

33

■507

8.

63.

212

. 'O

4

760

.28

34

499

9

64

202

10

1

•• 5

7i^

22

35

490

■

9

^A

192

10

; 6

710

18

36

481

9

66

182

10

; 7

692 12 j

37

47?

9

67

172

10

t

8

686

10

38

463

: 9

68

i6i

xo

9

676

•9

39

454

9

69

152

xo

lO

661

8

40

445

9

70

142

£1

II

6SS

7

41.

436

9

7«

^3^

•

12

646

6

42

427.

10

72

t20

11

13

640

6

43

417

10

72.

109

11

H

634

6

44

407

10

74

98

10

-15

628

. 6

45

397'

10

75

88

to

}

i6

622

6

46

387

10

76

78

10

I?

616

6

47

377

10

77

68

10

i8

610

6

48

367

10

78

58

9

»9

604

6

49

.357

II

79

49

8

■20

598

6

50

346

II

80

4»

7

r2I

592

6

51

335

II

81

34

6

22

586

7

52

324

II

82

28

5

-23

579

6

53

i»3

II

83

23

4

.24

573

6

54

302

10

84

»9

4

25

5<^7

7

55

292

10

85

15

4

26

560

7

56

282

10

86

II

3

27

553

7

57

i72

10

<

87

8

3

28

546

/

58

262

10

88

5

2

29

529

:, 8

59

•252.

10

^■9

3

2

' 30 t 53'

•8

60

.24*

lO-

I90

1-1 I 1

.1

APPEND! X/

jai

TABLE IV.

fifeevrlngthe PrObibilitJes of Life at fJoKTft*
Ampton. See page 260, 261.

^ iPcTtona

Deer,

A»M»

Perfotii

Oscr.

. Perfoni

Deer.

J

^«^-) li«»f .

QfUh.

Ajw.

livin<(.

>l Ute.

•*«"• living.

otUfe.

f

ii49

300

31

428

7

62 187

8

I

849

f27

32

421

7

63

179

8

2

722

50

133

4«4

7

64

171

8

3

672

26

34

407

7

65

163

8

4

646

21

35

400

7

66

155

8

I
•

5

6^5

16

36

391

• 7

67

H7

8

•

6

609

»3

•37'

?86

7

68

»39

8

7-

596

10

38

379

7

69

»3i

8

8

i86

9

39

37*

7

76

123

8

9

577

I

40

365

8

71

115

8

10

57^*

6

41

357

8

72

107

8

II

564

6

42f

349

8

73

99

8

12

558

5

43

341

9

74

91

8

»3

5^3

5

44

333

8

7|

83

8

•

»4

548

5

45

325

8

>

76

75

8

1

J5

543

5

46

317

8

77

67

7

t6

538

5

47

309

8

78

6a

-7

»7

53?

5

48

301

8

79

53

7

18

5^8

6

49

293

' 9

8e

46

7

*9

522

7

50

284

9

81

39

7

^

20

5«5

8

51

275

8

82

32

6

•

21

507

8

52

267

8

83

26

5

22

499

8

53

259

8

84

21

4

•

43

49»

8

54

25J

8

85

17

4

24

483

8

55

243

8

86

»3

3

85

475

8

56

235

8

87

ro

2

26

467

8

57

227

8

88

8

2

1

27

459

8

58

219

8

89

6

2

1

28

45i

8

59

211

8

90

4

2

J

29

443

8

60

203

8

9»

2

I

1

;?o

4.Z5

7 61 1

iqc

« '9^ \

!_

I

I

T

3^4

A P PE N DI X.
TABLE V.

SbewingtheProbabilitiesofLifefttNoRWiCB.

See page 262.

Perfonl
living.

Deer.

of Life^

Ages,

l.%i'*i5.

Uecr. 1
of Life'

A get.

"85

j20

32

I

865

160

33

2

705

60

34

3

045

32

35

4

613

23

36

5

590

20

37

6

570

16

38

= 7

554

13

39

8

541

11

40

9

530

9

4«

10

521

7

42

II

5H

6

43

12

508

6

44

13

502

5

45

14

497

5

46

15

492

5

47

16

487

5

48

17

482

5

49

18

477

5

50

^9

472

5

51

20

467

6

52

21

461

6

53

22

455

6

54

23

449

6

55

24

443

6

56

25

437

6

57

26

431

7

58

27

424

7

59

28

417

7

60

29

410

6

61

30

404

6

62

~Vf9\ -6 -j

392
386

380

374
368

g62

356
350

343

r337

33»

325
3' 8

3"

304
297

290

283

276

269

262

255
247

239
231

223

315
207

199

191

'83

6
6
6
6
6
6
6

7
6

6

6

7

7

7

7

7

7

7

7

7

7
8

8

8

8

8

8

8

8

8

9

Agu.

63
64
65

66
67
68
69
70

71

72

73

74

75
76

77

78

79
80

81

82

83
84

85
86

87

88

89
90

9'
92
93

Pcr£»M|

Deer.

iiTing.

ofUfe.

174

9

165

9.

156

9

147

9

138

9

129

9

120

9

III

9

102

8

94

8

86

8

78

8

70

8

62

1

7

55

7

48

6

42

5

37

5

32

' 4

28

4

24

4

20

3

17

3

14

3

II

2

9

2

7

2

5

2

3

2

I

I

1

I

. - .

t..-.^;. ^

APPENDIX.

325

TABLE VI. (a),

*

Shewing the prcfent Values of an Annuity of i /.
•on a Single Life, according to Mr. De Aiohre^s

hypothecs ; and» therefore, nearly, according to
. the probabilities of life at Brcslaw, Nor wica,

^nd Northampton. See p. 2, and p. 267.

Age.
8

3p«rCt.

3iperCt.

4perO<<

4|perCc.

5 per Cc.

6 per Ct.

i9»736

t8,i6o

16,791

» 5^595

M,544

I2,79Q

9

i9»868

18,269

16,882

15,672

14,607

12,839

lO

•

If

19,868

18,269

_^ p

16,882

15,672

14,607

12,839

1 i>799

19,736

18,160

16,791

>5»S95

M,544

12

19,604

18,049

16,698

«5>5«7

14,480

12,741

13

1^469

» 7^937

16,604

«5>437

14,412

12,691

14

«9»33«

17*823

16,508

»5j356

»4»342

i^^39

15

19,192

"7*707

16,410

'5>273

»4»«7«

12,586

16

19*05^

17.588

16,311

15,189

M9«97

12,532

>7

18,90$

«7.4<5?

16,209

i;,i02

14,123

1 2,476

18

18.759

17.344

16,105

15,015

14)047

12,419

»9

11^,610

17.220

»5>^9

H»923

«3>970

I2,j6l

20
21

1«,458

»7»<^93
16,963

15,891
15,781

14,831

13,891

I2,}01

18,30s

»4»737

13,810

i2,i39

22

18,148

16,830

1 5,669

14,641

«3j727

12,177

^3

i7>99o

16,696

>5»554

«4>S43

1 3,642

12,112

M

17,827

«^.559

«^»437

M>44«

13*555

12,045

»5

I7»664

16,419

15,318

M>340

1 3,466

11,978

26

17*497

16,277

«5>«97

M>*35

>3>175

il,t;o8

«7

17.327

«^.«33

'S»o73

14,128

13,282

11,8^7

28

17»»54

>S»98S

14,94^

14,018

13,186

11,76^

»9

1 6,979

>S.83S

14,816

13,905.

i3,oS8

11,688

30

16,800

15,682

14,684

«3»79«

12,988

n,r>^o

1

11^^530

16,620

iy,526

M,549

> 3^673

12,855

3^

16,436

« 5^367

14,411

"3»5S3

1 2^780

IIJ449

1 33

16,248

15,204

«4>2>o

.."H??

J?A7?

»m6«;

{a) This Table is the fame wiih Mr. De M^ivn*s Table of
the values of tingle lives, pablifiicd in his Treaii/e on Life
Jtmuities. and earned as far as the age of 79, to three places of
decimals, hy Mr. figj/on in his Mathtmaiical Repofiierj^ vgK U.
p. 169.

- ■ -. Y 3 •

3«6

A P P E t^VfX.

r #

TABLE .VI. Contiaued.

Agict 3 per Ct,

34

35

36

37
38

39

4©

4«

4*

.43

» 44

45
4^
47
48
49
50

5«

5«
5-3
54
55

56

57

58

59
60

16^57
15,864
15,666

>5f465
15,260

»5»oS3
14,842

14,626

M»407

Ht»B5

»3»95S

13*728

»3»493

»3»^54
'13,01a

12,764

12,511

12,255

IN994
11,729

IW45F
11,183

10,902

10,616

»o,325
10,029

9*7*7

64
62

63

64

!5
66{

67
68

69.
70 1

9t4»9
9^107

8,787
».4^?

«,r32

7»794

7*450

7*099

6,743
6,378

« 5^039

14,871

14,699

14.524

>4»345
H»^63

i3»97^

■ *■ i' » ■ I I J ' » ' ' J

3{ per Ct. 4 per Ct. a\ per Ct.

^^

"3*789
13*596

> 3*399

»3*i99

12^93

12,784

» 2.354

12,131

11.904

11.673

««f437

M.I95

• ic,95o

lOfc^S

.^ 0,443

10,181

9>9»3
9,640

9»36'i

9,076

8.488
8,185

7*87?

7*558

7**34
6,902

6.565
6,219

*••■

14,126

"3*979

13,829

13,676

»3r5'9
13*359
1 3*296

13,01s
12,858.
12,683
12,504
12,322

>2,i35
"*944
11,748
11,548

11*344

".»35
10,921

10,702

10,478

10,248

10,014

9*773

9*527

9*275
9,017

'3*304-

«S>»75

13*044

U.909
12,771

12,630

12,485

5per Ct.

»2r337
it,ct85

12,029

11,870

11,707

11,540

11,368

11.192

ll,Ol2

10,827

10,638
10,445
10,245
10,039

9*829
9.614

9*393
9,166

8*933

8,694

",705
11*570

»»*43'
iM^

11.142
10,992
10.837
10,679
10,515
10,348

8,753

8»48s
8,205
7,921
7,631

7*333

7|027

6.7 H

6,394

6,065

it^ '^'

8*44<^'
8.197

7.938
7,672

7*399

7*««9
6,831

6*534
6,230

S*9«8

10,176

9*999

9*817
9,630

9*437

9»239

9,036

8,826
8,611

8*389

■" ■ ■ — ^

8,161
7,926
7*684

7*435
7.179

6,643
6,362

6.073

5.77";

">*S99

: 10^90

iw,378
10,363

10. H4

19,021

9*895

^*76S
9**30

9*492

9*149
9,foi

9*049
8.891

8*^29]
8,561

8*587
3. 208

3,023

.7,831

7*633
7*428
7,216

6,770

6535

6^292

6,040

5*779
5t5o8 l

y^

T A BIL E Vt. Cbntintted.

' >l " ■ ■ 'IT I

8

69Q0S

4*453
4,046

3>6«2
3>*o7
2,776
2,334

r,42^
0,484

O^QOO

5,505
5,^3*
4,759
4^373
3,978

3,57r

8,741
2,309

1,867
1,411

P,955

0,000

]5?cEr

5»728

'5,3^3
5,029

4,666

4,293
3,912

3,52^

3,«"

2,707
2,a84

i,8so
1,406
0,950
c,4^i
0,000

4|pttCt,

5,596

4,926

4,55^

4,2«7

3,847

3,467

3,076

2,673
2,259

1,83^

>,394

0,943

0,479
0,000

5 p«rCt,

. '^468 .

5,»S2
4,8a6

4,4«^
4,H3
3,784
3,f»T
3,034
2,64*

2,t35

^ti6

',384

0,937
0,476

0,000

7p»cr

5/?28

4,$37 1
4,636

4,324
4a<poo

3,664

^,3»5
^,953
f*,578
0,188

1,783 .
5,362 1

0,925

f>,472
bfOOO

■ i

* I

Y4

1! A ^ L B

3i8

A P P E N D IX
TABLE VII;

t %

I

Shewiiig the Value of an Annuity on the jdint £bB*
tinuance of Two Lives, according to Mr. Be
Moporfs Hypotbefis\ and, . therefore, nearly^*
cording- to the probabilities of life at 9RESLAir,
NoiwicH, and Northampton. See Efiby IK
and p. 2, 3, 231, 267.

^ ^

1 ' '«/> ■ '

n

<
JO

«8

15.206

13-342

11-855

15

14,878

i3°93

11.661

20

14-503

12.808

111.430

^

«5

14.074

12.480

.11.182

10

30

13-585

12.102

10.884

35

13.025

11.665

10-537

40

11.381

II. 156

10.128

45

11.644

10.564

9.646

50

10.796

9.871

9.074

55

9.822

9.059

8.391

60

8.704

8.105

7-572

65

7-417

6.980

6.585

70
»5.

593^

5-652

5-391

i4'574-

i2.86q

11.478

20

14.225

12.593

11.266

25

13.822

12.281

11.02Z

'

30

13-359

11.921

10.736

35

ia.824

11.501

10.402

«5

40

12.S07

11-013

10.008

45

It. 496

10.440

9-541

50

10.675

9.767

8.985

55

9.727

^■975

8.318

60

8.632

6.041

7-515

•^5

7-377

6.934

6.544

70

5-9^2

5.623

5-364

APPENDIX.
T A 8 L 6 Vir. Continued.

325

**' .

«

♦* -

■^^ •

«*^ • 1

!l

til 1

:J1

n

JS.*

20

13.904

12.341

. 11.067

25

'3-53I

12.051

10.840

«

30

13.098.

11.711

10.565

9

35

12:594

11,314

10.278

40

12,008

10.847

9.870

20

45

.11.325

iQ.297

9.420

50

10.536

9.648

8.880

55

9,617

8.879

8-233

■

60

8.549 .

7.967

7.448

65

7.308

6.882

6-495

,

70
. 25

5.868'

5-590

5.333

13.192

1 1.786

10.621

30

12.794

1 1.468

10.367

35.

i4'333

11.095

1D.067

■

40:

11.776

10.655

9.708

25

45

11.130

10.131

9.278

50

10.^74

9-509

8.761

'

55

9.488

8.766

8.134

60

8.452 *

7.880

7-37^

•

65

7.241

6.826

6.440

.

70
30

5.826

5-551

5-294

1 2..434 ,

11.182

10.133

35

12.010'

10.838

9-854

*

40

11.502

10.428

9514

45

10.898

9-936

9.11a

30

50

10.18^;

9-345

8.620

55

9-338

8.634

8.018

60

8.338

7-779

7.280

65

7.161

6.748

6.373

70

, ^777

5'P5

. 5-254

f S5«>

T A B ^ E VII. Coptkiucd;

t

e m

35

^T"

40

45

50

o

:3ff
40

45
50
55
6q

65
7P

1— »•

11.632
11.175
10.622

9'955
9- 1 56
8.202
7.066
5.718

40

45
50

55
60

H
70

ia777
10.283
9.677
8.936
8.038
6.951

5646

45
50

55
60

65

70

50

55
60

65

70

?p3

9'33i
8.662

7-83«
6.807

5-556

8.892
8.312
7.568
6,623

5-444

55

55 ^

65

21

7.849
7.220

6-379
5-29'

:<3

10.530
10.157
9.702
9.149
8.476
7.658
6.662

5-450

9.826

9.41 8
8.9 1 1
8.283

7-5'P
^■55P
50^

9-063
8.619
8.044.

7-33!2
6.42)5

5'3op

8-235
7-738
7.091
6.258

5:191

7-332
6.781

6.036
5-053

9.600

9291
8.913

8.450

7.879
7.172

6.294
5'203

■ ■ ■ ly

9,014
8.671
8.244
7.7m

7-039
6.198

«-37o

7-987!
7.50a

6.875

6.o8d

5-063

7.660

^23o|
6.664.'

5.926!
4-9641

6.873
6.386

5-724
4-833

■I*

A PP EtT D.I X.
TABLE Vlh Coottnued.

33

1^

H

I t" ■ ■!

60

65

70

^

I .♦

I . «

60

65

70

lp»»*

65

70

22,

> ^

6737.

d043
5.08 J

5-547
±773

447<>

•-^

5'-730
.4-858

5-277
4-57'

4-I04.

«/»

It

• t

6.001

■.5-444
4-653

5.031
4.385

3-95?
.1. «. -*

•

TABLE

•3^»

A P P E N D IX,

TABLE VIII.

Shewing the JProbability of the Duration of Life in
London, deduced by Mr. Simpfon from obfcr-
vations on the bilb of mortality in Lon don fbt
10 years, from 1728 to 1737.

A ^M^

Perfoni

Deer.

Pcrfoiw

Deer.

PerlMSl Deer.
)iTing.]of Life.

Ages.

Imng..
1006

of Life.

320

Ages.

27

liviufC.

of Life.

Agcc.

54

321

6

135

6

I

680

^33

28

315

7

55

129

6

2

547

51

29

308

7

56

123

6

3

496

27

30

301

. 7

57

117

5

4

469

17

3*

294

7

58

112

5

5

452

12

32

287

7

59

107

5

6

440

10

33

280

7

60

102

5

7

430

8

34

273

7

61

97

5

8

422

7

35

266

7

62

92

5

9

415

5

36

259

7

63

87

5

10

410

5

37

252

7

64

82

5

11

405

5

38

245

8

65

77

5

12

400

5

39

237

8

66

72

5

13

395

5

40

229

7

67

67

5

14

390

5

41

222

8

68

62

4

15

385

5

42

214

8

69

58

4

16

380

" 5

43

206

7

70

54

4

17

375

5

44

199

7

7»

50

4

18

37^

5

45

192

7

72

46

4

»9

365

5

46

185.

7

73

42

3

20

360

5

47

178

7

74

39

3

21

355

5

48

171

6

75

36

3

22

35^

5

49

165

6

76

33

3

23

345

6

50

^59

6

77

30

3

24

339

6

51

^53

6

78

27

2

.25

333

6

52

147

6

79

25

26 327

6

53

141

6

AP'P E N DI X.

3S3

TABLE IX.

• •

Shewing the ExpeSations of Life in Londok^ ap-
cordipg to the preceding Table. See Mr. &mp* .
fon*s Scleil Exercifcs^ p, 255.

A«e.

Expectation.

Age.
28

Expe&ation.

1 Age. 1

55

Expedation.

I

27.0

24.6

14.2

%

32*0

29

24.1

56

13-8

3

340

30

23.6

57

134

4

35-^

31

23.1

58

«3i

5

36.0

32

22.7

59

12.7

6

36.0

33

22.3

60

12.4

7

35-8

34

21.9

61

12.0

8

35-6

35

21.5

62

11.6

9

35-2

3^

21. 1

63

JI.2

10

34.8

37

20.7

64

10.8

n

34-3

38

20,3

^A

10.5

12

33-7

39

'99

66

10. 1

13

33-1

40

19.0

Po

9.8

-14

32.5

41

19.2

68

9-4

15

31-9

42

18.8

69

9.1

16

31-3

4J

18.5

70

8.8

»7

30-7

44

18.1

71

8.4

18

30.1

4^

17.8

72

8.1

«9

29.fi

46

17.4

73

7.8

20,

2».9

47

17.0

74

7-5

21

28.3

48

16.7

75

7.2

22

27.7

49

16.3

70

6.8

23

27.2

50

16.0

77

6.4

24

26.6

51

15-6

78

6.0

25 •

26.1

5«

15.2

79

S'5

26.

25.0

53

14.9

80

5.0

27_

25.1

54

14-5

APP EN D 1 X:

T A B L £ X.

• « *

SbewtDg the Value of an Annuity on OHi Life^ t€^
cording to the ProbabiUti|?& ot Life in LokdoK,

Sec Mr. Simp/on^ 5 SeleU Exercifesj p. 260.

*~"

Is

^i

Is

■Se

^^•

^^i

■3 s

"3-

•

•a<3

ii-s.

■i«3

i

fcV

•§c3

ta

^

tS

.4 Z

00

'3 »,

3 h

P t.-

&

3 4;

9 k.

9 u

&

^ ts

3»,

<

0. U

■ D*

;^S,

A.

<

'^•K.

flu

^s.

<j

'^S.

•^-^

V

« en

> 13

^t

6

18.8

^6.a

14.1

3»

14.8

12.9

ti.4

56

lO.I

^•'

8.4

J

18.9

?6.3

14.2

32

14.6

12.7

"•3

57

9.9

0.9

8.2

I5.C

i6.4

H-3

33

14.4

12.6

ii.2

58

9.6

!-7

8.1

.9

119.0

16.4

HS

34

14.2

12.4

II.O

^9

94

8.6

8.0

|0

19.0

^6.4

H'3

35

14.1

12.3

10.9

60

9.a

8-4

7-9

;i

19.0

^6.4

'4-3

36

13.9

12.1

10.8

61

8.9

8.2

7-7

12

18.9

J6.3I14.2

H

»3-7

II. 9

10.6

6i

8.7

8.1

.7.6

»3

J 8. 7

16.1

14.J

^

^3 5

11.8

10.5

63

8.5

7-9

7-4

14

18.5

16.014.0

99

133

II. 6

10.4

64

l^

7-7

7-3

»5

i«.3

15.8

13-9

40

13.2

n.5

10.3

6i

8.0

7-5

,7.1

t6

18.1

15.6

>3-7

41

13,0

11.4

ia2

66

7.8

7-3

6.9

»7

17.9

15.4

»3-5

4*

12.8

il.2

10.1

^Z

7.6

7»

6.7

ts

17.6

1st

»3-4

43

12.6

II. I

10.0

68

7-4

6.9

6.6

«9

17.4

iS-O

»3-2

44

12.5

II.O

9.9

69

7-1

6.7

6.4

fto

17.2

14.8

13.0

45

12.3

10.8

9.8

70

6.9

6.5

6.2

ki

i'7-o

14.7

1-2.9

46

12.1

10.7

97

7>

6.7

6.3

6*0

ka

e6.8

14.5

^2.7

47

II.OIO.5

9-5

72

6.5

6.1

5.8

h

16.J

14.3

12.6

48

II.8

1D.4

94

73

6.2

5-9

5'6

N

16.3

14.1

12.4

49

II. 6

lo.a

9-3

74

^1

5.6

5-4

f5
k6

2S

16.1

15.9
15.6

'5-4

H-C)
'3*

'3-4

12.3

I2.I

12.0

11.8

SO
SI

52

53

11.4

II. 2
II.

10.7

lO.I

9.S

75

.5-41

5-2

9.9
9.8
9.6

9.0

0.0

4

29

15.2 13.2

11.7

54

10.5

9-4

8.r

7r

1 s.C I'^.l

1 1.6

ii

10.'^ ?' 8.f|l f

A P P E N D I X*

Sis

TABLE XI.

Shtwing the Value of an AHiiuity on the joint con-
tihuance of T>k^. Lives, according to the proba^'
biHtics of Life, in Lokdon. Sec Mr, Simp/oifs
Selii^' Exefdfes^ ' p. 1 66.

•9 .

14.7

"Jtr

13.0

II. 6

c

as 3

-!»!-r

.»g

12.8

> *

"•3

*3

10. 1

>

lO

20

«5

14-3

12.7

11.3

25

12,2

10.8

97

20

13.8

I2.!2

10.8

30

ti.6

10.3

9.2

•

25

»3i

11.6

J 0.2

35

10.9

9.8

8.8

3°

f2.3

10.9

97

,40

10.2

9.2

8.4

lO

35

11.5

10.2

9»

20

45

9-5

8.6

7-9

■

40

ia7

9.6

8.6

50 :

8.8

8.0

7-4

45

lO.O

9.0

8.1

•

55

8.f

7-5

6.9

» •

50'

9-3

8.4

7-^

60

7-4

6.9

6.4

.

55

8.6

7.8

7-»

65

6.3

5-9

«

60

^•^

7.2

6.6

70

6.0

5-7

5-4

4

•

65

6.9] 6.5

6.1

75

5-»

5.0

4.8

70

6.1

5-8

5-5

75

5-3

51

49

25

11.8

10.5

.9.4

'

30

II-3

lb. I

9.0

i

i

15

^3 9

12.3

II.O

35

10.7

^.6

'8.6

20

'3?

1 1.8

10,5

■

40

lO.O

9.1

8.2

« •

•
* t

»5

12.0

tl.2

lO.I

45

9-4

8.5

7.8

30

1 1.9

10.6

9-5

25

50

8.7

7-9

7-3

*

35

tt.2

lO.O

9.0

55

8.0

7-4

6.»

a

40.

10.4

9.4

8.5

^ « •

•60

i;l

•6,8

6".3

'.$

45

9.6

8.8

.8.0

.4

'65

.6.2

5.8

-

50 •

8.9

8.2

7-5

«

70

5-9

:5.6

5-3

1

.55

•8.?

■

7.6

7-0

'
'

75

5-»

4.9

'4-7

^

;6o

7-5

7.0

6:5

.

, .

(

r^—

■65

6.8

6.4

•6.0

3<i

to.8

.9.6

8.^

70

6.0

5-7

5-4

3^

35

10.3

9.2

8-3

Ir-;

fi-2

/;.o

4.8

.40.1 7

8.8

8.0

336 APPENDIX^.

TABLE XI. Corifinucd.

V ,\ 1

c*» , ^ - 1

•^ .

w

«>

«** •

V . •#* 1

«i

It

IS ^

ft

c

«6

^1

■St

as

1^

<
45

9.1

8-3

*

7.6

< -^

<

6.3

5-8

5-4

' #

65

50

8.5

7.8

•7.2

45

70

5^

TJ

~5;d

^^^\.

55
63

7 9

7-3
6.7

6.7
6.2

75

4-9

4-7

4'5

30

7.2

65

6.S

6..1

5.7

50

.7-6

6.8

■

6.2

70

5-8

5-5

5-2

55

7-2

6-5

6.0

75

5-1

49

4.7

50

60

6.7

6.1

5.7

——

63

6.2

57

5-3

35

9.9

8.8

8.0

1

70

.5-5

5-*

4.9

40

9.4

8.5

7-7

75

4.8

4.6

4-4

45

8.9

8.1

7-4

—

50

8-3

7.6

7.0

55

6.9

6.2

S'7

35

55

7-7

7-1

6.6

60

6.5

5-9

5-5

60

7-1

6.5

6.1

55

65

6.0

5.6

5.2

65

6.4

6.0

5.6

70

5.4

5.1

4.8

70

5-7

5-4

51

75

4.7

4-5

4-3

75

50

4.8

4.6

60

6.1

5.6
6-3

5-2
4.9

1

40

.9»

8.1

7-3

6a

65

• S-7

45

8.7

7.8

7i| "

7Q

5-2

4-9

4.6

50

8.2

7-4

6.8|

75

4.6

4-4

4.2

40

55

7.6

6.g

6.4

i

65

•——

60

7.0

6.4

6.0

^

5-4

5-0

4-7

65

6.4

5-9

5.5

65

70

4.9

4.6

4-4

70

5-7

5-4

51

75

4.4

4.2

4.0

■

75

5-0

4.8

4.6

70

70

4.6

4.4

4.2

45

8-3

7.4

6.7

75

4.2

4.0

3-9

45

50

7-9

7-1

6.5

55

^+

6.7

6.2

75

75

3.8

3-7

3-6

■

60

6.8

6:,3

5.8

1

«

APPE rj b 1 JT; 3jy

TABLE til
Sliewiog the Probabilities of Life in Ld^DtiN, oii
the ^ppontion, that alt who die in London
Were born there; Formed f^m the Bills^ foir
ID years, from 1759 03 1768. See p; 250.

. — jsErrETT-

TXZ

ro^r-

^»^».| i)«,. 1

^fc.,.

rfUft.

A|rt.

BT«.

ifLlf«,

A|ti.

B.l,t Uufi.

1000

240

Ji'

404

9

f

1

760

99

32

395

9

e

2

661

4»

33

386

9

6

3

619

29

34

377

9

6

4

590

21 '

35

368

9

e

5

569

II

36

359

9

t

6

558

10

37

350

9

6

7

548

7'

38

341

9

6

8

i4>

6

39

332

10

7

9

535

40

322

ID

?

10

53°

4'

312

ID

>

11

526

42

302

ID

>

12

522

43

292

ID

7

■3

5"8

44

282

ID

7

14

515

45

272

to

7

15

512

46

262

ID

7

16

509

47

252

ID

7

■7

506

48

242

9

7

18

503

49

233

9

8

«9

499

50

224

9

8

20

494

6'

215

9

8

21

487

5"

2d6

8

8

32

479

53

.98

8

8

23

47"

54

190

7

8

24

463

8

55

183

7

8

is

45S

8

56

176

7

8

26

447

8

57

169

7

8

^7

439

8

58

162

7

8

28

431

9

5»

155

8

9

29

422

9

60

'47

.8

30

41?

9

61

'??

■ r.

_

3S«

APPENDIX.

TABLE Xm.

Shewing the true Prob^Hittes of Life \n Lohdok
'till the Age of 19. See p. f 54. -

A(e.

O
I
2

3
4

5
6

7
8

9
10

II

12

«3

14

«5
i6

»7
18

>9

20
21

!■ I

411

340-
319

298
291

28j;
286
276
27a
268
265
262

259
256

249

494
487

Decrrments
of Lifc.

240

99
42

29

21

II

10

7
6

5

4
4
4
3
3
3
S
3
4

The numbers in the fecond column to be coo-
^nued as in the laft Tabk.

3«

A B^ B.NiJix.

TABLE XIV.

^tiewing the ihtt Probiibiliti^ of Life Ih LoitDarir
fir all Ages, fbrined from the BtlU for lo yean,
from 175910 1768. ^ttp. 256.

pii.

-s.,. , .

-fflS

Tcr

"^~"

pJXT

o„,.

A|*l,

ii.i«.

of Life

Age

u«a.

DfUft

Ajei

liviot.

ofUCt.

■s.s

486

9»"

♦°4

»

ST

13a

7

t

1032

200

32

lU

S

63

125

7

3

«32

85

33

9

64

I18

7

3

747

59

34

377

9

65

III

7

■f

683

42

35

368

9

66

104

7

5

646

23

3»

359

9

«7

97

7

6

623

2S

!?

350

9

68

90

7

I

603

14

341

9

65

83

1

. a

589

12

39

332

10

70

76

9

^V

lb

40

322

lO

7>

70

6

10

567

9

4"

312

ro

72

64

^

II

558

f

4>

302

10

73

S8

5

11

549

43

292

10

74

53

5

'3

541

7

44

282

10

75

48

5

14

534

6

45

271

10

76

43

5

'5

528

6

46

262

10

77

38

5

16

522

7

■*2

252

10

78

33

4

17

S"5

V

4«

4

i3

508

7

49

3

■9

501

7

50

3

W

494

7

5-

3

21

487

8

52

3

22

479

8

53

2

23

471

S

54

2

24

463

S

55

2

M

455

e

j6

2

26

447

8

57

1

27

439

8

58

1

28

431

9

59

.- 1

29

422

9

60

3°

413

9

61

340

A:P P.E.N- OI.X*
T A B LE XV.

Shewing die Value of an Annuity on the longeft of

Two given Lives, according to the Probabilities

■ of Life in London-. . Sec Mr. Simf Jen's SeieQ

ExireiJ

M, p

268

If

M

11

£1

E

1

ii

1

II

lO

I7.I

19.9

23.4

20

■ 5-8

■ 8.3

21.6

■5

16.8

19.5

22.9

25

'5-5

17.9

2^.^

20

16.6

19. 1

22.5

30

■53

17.6

20.7

25

30_

■ 6.4
16.2

18.8

i8.6

22.2
2^

35.

iid

■7-4

20.4

40

45

■ 5.0
■4-9

17.2
■ 7.0

20.1
19.9

35

16.1

.8.4

2^.6

40

16.0

■ 8.3

2>-4

20

50

'4.7

16.8

■ 9.6

D

45

15.9

18.2

2^.2

55

■4-5

■ 6.6

'9 4

50

.5-8

18.0

20.9

6^

■4.3

■6.3

19.1

55

■5-7

.7.8

20.7

«5

70

14.1
■ 3.8

■ 6.0
■5-7

■8.7

i8.a

fo-

'5-5

■ 7.6

204

«5
70

>5-3
15.1

'7-4
■ 7.2

20.1
19.8

21

'3-5

■5-3

1£7

25

■5'

'/•4

20.3

75

14,8

■ 6.9

i2i

30

14.9

.7^

■9.S

'5

16.7

■ 9.3

22.8

35

»4-7

■6.7

19.4

ao

.6.4

■ 8.9

22.3

40

■ 4.5

.6.5

■ 9.2

>5

16.2

18.6

21.9

45

•4-3

.6.3

.8.9

30

35

16.0

■8-3

21.6

2r_3

i5

50_

■4.2

16.1

.8.7

15.9 '8'

55

14.0

■59

.8.4

40

'5-7 '7-9

21.1

60

■ 3-8

■ 5.6

■ 8.0

5

45

15.6 1 7.8

20.9

65

.36

'5-3

■ 7.6

50

15.4 1 7.6

20.7

70

13.3

■5-0

17.2

55

■5.317.4

20.4

IL

li?

14.6

iiz

60

15.2117.2

20.1

30

■4-«

■ 6.6

•9-3

6i

15-016.9

19.8

30

35

J 4.2

■ 6.2

.8.8

70

14.716.6

■ 94

40

140

15.9

.8.4

!

.2£.

i-iji6.,

.8.9

45

13.8

,5.6

.8.1

^^

A Vf E N I) I JC.

34«

TABLE XV. Continued,

"5^

« g

30

•S .

o
if

u,^>

25

. , \

40

■

45

50

55
66

35
40

45
50
55

^o

70

40

45 4
50

55

60

65

70

75ji

45
50

55
60

w^

ft i

34\
3.2

2.6

2.2

3^
3'-5
3-3

2.7

2.4

2.0
i.6i

" t

3-3

3-0
2.7

2.4

2.1
1.8

1.4

I.Q

2.8
2.5
2.1

»-7

5i4

4.&

4-5
4.1

3-7

5.8
5-41
5.1
4.8

±B

3-8

3"<i

if
5.0
4.6
4.2

3-5

3»

2.7

2-3

4.2

3-8
3-4

e c

CO

7.8

7-4
7.0

6.6

6.1

£-
8.3
7.8

7*4
7-»
67]

6.3

5.8

5-3
14.8

7-3
6.8

i€.3
5-9

5-4
4.9

4-5
40

6.2

5-7
5.2

4-7

45

50

65
70

P75

55

mm

60

65

70

75

50

5$
60.

70

II

55
60

65
70

75_

60

65
70

75

65

70

21
70

11
75

lv4
IiP

0.6

I

i.i

0.5
o.i

1-3

0.9

0.5

0.0

9-5

0.5
0.0

9-5
9.0

9.4
8.9

ll
8.2

If

6.9

a

2.5

2.0
1.6

3'3
2-9
2.4

2.0

r-5
i.o

2.4
1.9

»-3

0.8

1.2

0.6
0.1

9-5

1 0.0
9.4

i2

8.6
7-9

7.2

4.1
3.6

111

5-0
4-5
£9

3-3
2.8

If

3.6
3-0

2-4

1.8,

1!

2.2

'.5

0.9

11
0.7
0.0

9^3

9.2
8.4

7.6

f

Z3

34?

i^ff^^P^Mr

TABLE XVI;

Shoving the Value of an Aaouiqr oa the long»ft ci

■ Two Lives, according to Mr. Pe Moivre's By.

potbtfis ; and, therefore, nearly according to the

probabilities of Life at Bk.xbl'aw, Noevich,

and NettTHAUPTON. See Fi^ *$i, 167, 26^.

24-53

23.82

23.08
22.71
2«'33

21-58
21.23

20-58
20.3
23.81
23.42

.03
22.63
22.23
21.83
21.42
21.03
20.65
20.29
'9-95
19-^4

20.42
20.20
19.96
19.72
19.46
19.20

~ 9^
18-64

18-35
18.07

17-79
'7-53

7-30
19.96

9.71
19.45

9.17

'7-3'
17.22
17.07

6'.
16.71
16.52
16.31
16.10
(5

'5-%
15.42
15.30
■4.99

17.06
16.89
16.7
16.52

. ''-J'
8.59 16.10

18.29

18.00

'7-

17-38

17.11

16-85

15-63
15.40

'5-'5
14-91
14.68

eo|23,Di
2-59

3.l£
1.73
1.49
<>.S£:

■43

19.44 i6>79

50 20.

9-^i
19. 2I

8-97

19-16

18,86

S5

(8i?4
7.92

17'5!

!'i94
16,64
16.31

6.52
16.31
16,06
i;.86
15.61
''5-36
15-10
14-83
(4-57
'4-33

■9-85
■8-53
18.20
17-86
45 2as6 17.51
5019.8017.15

35

2.14
1.67

2I.£0
13

9-36
8.94 16.

16.31
16.09
15.85

»5-59
'5-33
15.05

18.55

l8.22

16.80 I4.77
14.48

14.2a

■45
6.12

I5-83H3-95

A P P 1: N D t X. ^ 343

TABLE XVL Continued.

3

%

28

<

tn

30

30
3520

40

45
50

21.16

20.14
19.63

»3

19.1
xfk6

(<55i

L2S

41

'9
17.77

35

40

U5
40

45
50

55
60

40

45
I 50

55
60

65

45

70

45
50

55
60

65

70

20. 10

^953
i8.97

18.42

17.89

>7-39
16.93

16.52
18.91
18.29
17.67
17x39

'6-53
16.02

\5-57

^7-59
16.91

16.25

15-62

15.05

i ^'55

II.
■§t>

!J JIH?

8.18
7.82

7-451
7.07

6.68
^•30

5.56
5-^4

7-43
7.02

6.60

6.17

S-76
5-34
4.95
4-59
6.56
6.10

5-^3
5.16

4.70

4.27

3-88

5.58

505
4.52
4.01

3-53
3.01

5.84J
5.58

54^
5.02

4.72

4-4«:

4.1011

3*79

^o

55

60

70

5-30
5.00

4.68

4'35L
4.0o[ 65

3.66

3-33I
3.02

4.66

4-3»
S-94-

3.56II

3.»9
2.82

3-91

3-50
3.08

2.65]
2.24!

1.85

ft'

50

55

65
70

55
60

65

It

16.13

»5-38

'60J4-67

14.02

'3-45

70 12.27

(>5

70

i4»5a
13.69

12.93

li

ulf . 1

"S IT

14-45
13.85

t3.l7

12.72

12.21

13.03

12.07
11.60
11.16

60 12.72 11.68
65 11.81 10.92
70I11.02 10.22

10.72

^o\ 8.48

13.16
12.48
11.84

11.26

9.98
9.12

8.02

12.00
11.44
10.89
10.38

10.78

10.12
g.51.

9-33
8.57'

7.60

'

■..•■

* **■

?4

OBSER-

344 APPENDIX*

ppSfERVATlONa

pif

TABLES I, aqd |I,

i

THESE Tables may be met with ii|
moft of the books that treat of topiT
pound intereft and annuities ; but there ha$
been, in this work» fo much occafion for re-
ferring to them^ that it wa$ neceifary to fara
the reader the troifble pf tur|iin^ to other
books for them.

The 2d9 3d, 4th, &c. nuni(bers in thp Second
Table, are only the /urns of the iirft 2, 3^
4, &c. numbers in'the Fi^ T^blc. This
Table, therefore, is the foundation of the
^econd^ and, indeed, of all the commoq
fables of compound intcred ; and, with the
help of it^ almoft all the queflions^ in com--
pound intereft pay be eafily ^nfwered^

The following fpecimen of this may, |
thinks ^e pf pQn^derab|e ufe.

QuESTioBT I. ♦* To what J^w or annuity
" will any given fum or annuity^ now to be
*' laid up for improvenient, at a given rate
^* of compound intereft^ increafe, in a given
^ number of years ?"

APPENDIX. 34^

ANSWER. Divide the given fom or an-
nuity by the value of j /. payable at the end
of the given number of years, and the qut^^
(tent will be the anfwer.

Exaipple, • Let the given fum be -50-/. and
iSxt given time 1 8 years . The rate of intereft
4fer cent. -^Thc prefent value, at 4 per cent.
or I /. payable at the end of 1 8 years is, by
Table I, .4936 j and 50 A divided by this
value^ gives /. 101.296, or 1 01 A 5/. xhtjiim
to which 50/. will in^rreafe in 18 years. In
like n^anner ; 2 1, per annum^ the nrft payment
of which IS to be made immediately, will
be increafed (int6reft fuppofed the fame) at
the end of 18 years, to an annuity of /. 4.05 :
for 2 /. the given annuity, divided by .4936,
gives /. 4.05, or 4 /. i /.

Question II. ** To what y»w vvill a
f^ given annuity ampunt, in confeqpence of
^* being forborn and improved, at a given
^^ rate of compound intereil, for a given
^' number of years ?"

Answer. From the increafed annuity,
found by the ]aft Queftion, fubtradl ^^ given
annuity ; and multiply the remainder by the
PBRPETUfTY, and the produSi will be the
^fwer.

Example. 2 Lper ann. improved at ^per
fent. compound intereft, will, by the lafl
Queftion, increafe, in 1 8 years, to /. 4.05 per
gnu. 2 1. fi)btra£ted from 4.05, leaves 2.05,

. which.

75*6 Al>PEND1lL

^liich, taliltiplied by 25, the perpftmty^ ^ves
/: $i^^S* ox SI I- 5 A tho amount ift 18 yeaa.
In die iame manner it may be foand^ that
10 A per ann. (intercft being, the fame) will
amount, in 41 years, to 99$/.

It (hauld be remembered^ that the pj^Jt*-
PETUiTV i$ 33.33> — 28,57,— 25^-^a9t'-^r
j6.666» accofding a^ intoreft is reckoned at
3,*7-t3,f ,i— 4,T**5 or 6 ^r r^/; Aha. that the
annuity meant in all thefe Qjie&ions }^ an
miluity, the fixfl payment of which is to he
ona^ie immediately.

Question III. " In what number of
'* yc^rs will a given fum ,or annuity incrcafis
*' to another gvitnfum or annuity, fnconfe*-
** qiicnce of being improved at a given rate

'' of intercft?"

• • •

Ais^swER. TiWv^t xht original fum or an^
nuity by the increaj^d Jum or annuity ; and
look for the quctient, or the number neareft
to it in Table I; and the number of years
correfponding to it wilLbe the anfwer.

Example. Let t)[ik> funt be 50/- The in-
creafed fum A i o j .29. The rate of intereft,
4 per ant. The former fum divided by the
latter gives .4936, which (lands oppofite in
the Table to 18 vears, or the time in .which
50 /. will gain the required incrcafe.— -In
like manner, it may be found, that i8 years
is the time in which 2 /. per ann. will increale
.to /. 4.05 per ann.

Question

AFP;EN?DIX, 347

* QgssTiov'IV. '^ la what tkne will any
i< giycsx annuity amount to a given Jum^ ia
f* cpnfequence of being forborn/iind inv-
f ^ provedi njt a ^iven rate of compound in-
V tereft?'

Amsw^r. Divide the giveoy^i;? to which
^hc annuity tpuft amount by the peupbtit^
JTY. Add the given annuity to the quo-
tient ; and by the quotient fo increafed» di*-
3^ide tfa^ giv^n annuity ; and iici\% fecond itpith-
ftent^ found in Table I. will fhcw the a»-
fwer.

Exsunplef A perfon owies loooL and re*
.^v<s (p appropriate lo /. per annum of his
JACorpe towards difcharging it> le what
pme yirill fuch an appropriation^ in confe-
quence pf being improved at 4 per cent.
amoi^nt to a fum equal to the debt ?
)090 A divided .by 25 gives 40 /. 10 L added
to 49/. makes 50 /; and 10/. divided by 50/*
gives .2900^ which in the Table (lands op*
jpoiite to 41 yearS) the rcquired time*:

In ;he' fame manner it will appear, that
the fame annuity^ if improved at 5 per cent.
will amount to 1000/. in 37 years*

Question V. f* In what time will a
<^ gi^i^n principal be annihilated^ by taking
f ^ oat of it» at the end of a year, a given fum,
f f and after that, the fame fum annually, to-
ff geihar with its growing intercfts f "

7 An-

\

348 APPENDIX.

Answer. In the fame time' plainly in
'^bich an equal Annuity would amount to the
;given principal.

•A perfon, therefore, poflefs'd of looo/.
capital, bearing intereft at 4 per cent, would^
by Queftion IV. reduce it to nothing in 41
years, by taking out of it 10/. at the begin-
ing of the firft year, and as much more every
following yfcar, as would be neceffary, to-
gether with the intercft of the remaining
capital, to make his annual income conflant-
1y 50 /•

•fteiiiatk. The fum to which z given an-
nuity will amount in a given time, is the
fame with the value of an annuity for the
given tiitie, equal to the given annuity in-
creafcd by the yearly intereft of the amount.
That is, f 000 /• is the value of 50 /. per ann.
for 4 F years at 4 per cent : And the fiiinc
futfi is likewife the value of 60 /. per annum,
for 37 years at 5 per cent. The reafon is
plain:- 1000/. it has appeared, would, in
confequcnce of being put out to thefe dif-
ferent rates of intereft, be juft fufficierit to
pay the annuities.

I have been the more explicit in thefe
rules, becttufe they point out a very eaiy
method of deducing and examining all I have
faid, in different parts of this work, and
particularly in Chap. III. concerniifg the in-

creafe

APPENDIX. 349

creafe of. jnoncy at intereft.*-*— -I will jufL
mention ond inftance.

400^000 /. fier annum^ applied in the man*
ner fuppc^ed in Qgeftions iV. and V. would
annihilate 55 millions^ bearing intereft at 5
per cent^ iii 42 years.

In 171 6> when xhc Jinking fund was efta-
bli(hedf ^e public debts were near this fum,
And bore 5 per cent, intereft. This fund then,
bad but 400,000 /• of it been inviolably ap«
plied to the annihilation of the public debts,
would, in 1758^ have difcharged all the debts
con traded before 1716.— — And it may be
further found very eafily, by the 'anfwer ta
Queftion IV. that had it been fuffered to go
on in its operation, and been applied, fnce
1758, to the redemption of only ^per cents
at par^ it would by this time have difcharged
104 millions; and feven years hence 140

millions. The aiTertion, therefore, in

page 165, is atxi&Xy true. But the following
proof of that aflertion will, perhaps, be more
clear and flriking.

Suppofe an annuity of 400,000/, beginning
in 1716, to have been applied UN alien--
ABLY till J 730, to the annihilation of debts
bearing intereft at 5 per cent ; from 1730 to
1748, to the annihilation of debts bearing
intereft at 4/^r cent, and from 1748 to 177 1,
to the annihilation of debts bearing intereft
at 3 per cent. In the firft of thefe periods th«
annuity would have increafed to 8oo,oooA;

in

I

3*>

APF EN D I X.

in xhtjeeondy to 1,600^000 A i ia tbtf Idfi^ ib

3,200,000/. In the laft year, fh«refor«^

the nation might h«ve bcon eaied of above
fhree millions per annum in {soi^u A^ at tbd
fjUBC time, (Ibppodng all the ^laoe tneafurea
taken in other refpeds) it woi»ld ha%^ ^n-«
joyed the benefit of the grealeft pa^l of tiiat
very Jinking fund it now ha« 5 and fla ^tri^
ment could have^arifen to the puUi^, froiii
any of the applications which have been madd
of it to coment expences.

I^IKZC'

AFPE.NPIX. ' 3^

*

Directions for finding the Va-
L V B s of two JointLivbs, and
of the LONGEST of two livcs.;
and alfo, of three Joint Lives
and the longest of three lives,
by Tables VII, XI, XV, and XVI.

3rF both the ages arc given in the Tables,
[^ the value wanted virill be found imme*
lately by infpeflion.
If the ages arc not given in the Tables, it
will be beft to proceed in the following man*
nen

Suppofe the rate of intereft ^percent, and
the vs^ue defired of two joint lives, whofe
ages arc 40 and 66. ■ ■ It will appear, from
infpedking Tabic VII. that the value fought
would be 6.556, wcrie the age of the elder
life 65; and ij-383, were it jq. Since,
therefore, it is 66,' the value nxuft be the
J&y? of four arithmetical means between 6-556
and 5.383, or 6^322. Fof the fame rea-
i(bn, had the ages of the elder been 68, thq
value would have been the 3d arithmetical
mean between 6.556 and 5.383 or 5.854.—
In Jike manner, were the prop^fed ages 43
and t^t the value would be the third arith-
axetkal lacao between 6*556 (the v^Iue of

tW0

352 APPENDIX.

two joint lives whbfe ages are 40 and 65)
and 6.4259 (the value of two joint lives*
whofe ages are 45 find 65) or 6.478.

Again, let the ages be 43 and 66. That
is, let it be fuppofed, that ne;ither of the
propofed ages is given in the Table.

The values correfponding to the ages

The value, therefore, correfponding to the
ages 43 and 66, muft be the 3d mean be-
tween 6.322 and 6.200, or 6.250.

N. B. The I ft, 2d, 3d, and 4th of four
arithmetical means between two numbers
are found by fubtracjli ng 4» t* Tf a^d 4 of
the difference between the two numbers, from
the greateji of them.

Thus. The difference between 6.556,
and 5.383, is 1.173. One-fifth of this dif-
ference is .234; which, fubtradled from
6.556, leaves 6.322 ; the firft of 4 means
between 6.556 and 5.383. — —In like man-
ner; the difference between 6.322 and 6.200
is .122. One fifth of thi^ difference is .024;
and^ therefore, three-fifths of this difference
is .672, which, fubtraded from 6.322, leaves
6.250, the third arithmetical mean betv^een
6.322 and 6.2cb.

In order to avoid trouble, if the ages are
nearly equal, a year or two rriay be added to
the Icaft, and as much fiibtradtcd ftom the
jjreateft i and the value taken by infpeftion.

But

APPENDIX. S53

But if one of them much exceeds the otheo
it will in general be fufficient toi take thd
nearefl; number in the Table fbr the IbiTer*

The mean betweeh the values at 3 per
tent, and 4 per cent, may be taken for the
Value at 3f percent* without any error of
confequence. And the like may be faid of
the values at 4! per tenti

The values of the longeji of two lives is
found by fubtrafting the value of the joint
lives from the ftitn of the values pf the two

Jingle lives. Thus, the values of two

fingle lives^ whofe ages ixt 2^ and 30; arc
by Table VI. (inteteft reckoned at 4 per
tent.) 15-31 and J4,68. The fiim of thefe
two values is 29.99.; the value of the joint
lives is^(by Table VII) ii.46i and this va-
lue, fubtradted from 29.99, gives 18.53; of
the value of an annuity on the longefl: of the
two lives.— ^By this rule, Table XVI. has been
calculated ; and a demonftration of it hiay
be found in Mr. Simpfon's DoBrini ofAnnu^
ities and Reverfions, page 20;

The value of two joint lives being given^
the value of three joint lives may be found by
the following rule^ taken from Mr; Bimpfon^i
Seleil'Exercyesi page 279;

Let A be the youngeft^ and C the oldeft
of the three propofed lives. Take the value
of the two joint lives B and C^ and find the

A a age

"n

354 A P P E N D I X.

age of a Jingle life D of the fame value*
Then find the value of the Joint lives A and
D, which will be the arifwer.

Example. Let the three given ages be
"25^ 30, and 40, and let the rate of intereft
be 4 per cent. Then the value of the two
oldeft joint lives B and C, will (by Tab. VIL)
be 10.4289 anfweringy in Tab. VI. to a fingle
life D of 54 years of age. And the value of
the joint lives A and D, which is 8.917
years purchafe^ will be the value fought.

From the value of three joint lives given^
the value of the hmgefi of three lives may be
deduced in the following method. — '* From
** the fum of the values of all xh^ Jingle
*' lives, fubtraft the fum of the values of
** all ih^ joint lives, combined two and two.
^' Then to the remainder add the value of
** the three joint lives; and this laft fum
** will be the value of the kngefi of the three
*' lives." See Mr. Simpfon's DoStrine ofAn^
nuitieSf &c. page 23— or Mr. Dodfon's Ma-
thematical Repqfitory^ Vol. I. page 244.

Example. The fum of the values of three
fingle lives, whoie ages are 25, 30^ and 40^
is (reckoning intereft at ^per cent.) 43.202.
The value of two joint lives, whofe ages are
25 and 30, is, 11.468; of /W0 joint lives^
whofe ages are 25 and 40, is 10.655; of
two joint lives^ whofe ages are 30 and 40, is
10^428^ by Table VII ; and the fum of thefe
• ^7 three

A P P E N t) I X. 355

ihtt6 Valdes is 32^551. This fum fubtra£led
from 43.202 leaves 10.651 ; which remain^
der added to 8.917 (the value juft found of
the three joint lives) gives 19.568, the va*
lue of the longeft of the three lives^

A a 2 SUP-

[ 3J7 ]

SUPPLEMENT,

CON TAINING

ADDITIONAL OBSERVATIONS

AND

TABLES.

SINCE the firft publication of this work^
I have had the pleafure of reading an in-
genious Memoir on the State of Population
in the Pats de Faud, a diftriift of thepro-
vince of Bern, in Switzerland. The author
of this memoir is Mr. Muret^ the firft mi-
nifter at Vevey^ a town in that diftrid, and
iecretary to the Oeconomical Society there.
It forms the firft part of the Bern Obfcrva-
tions for the year 1766 ; and a good abftrad:
of' it may be foand in the 69th article of a
work entitled, De re Bufiica, or the Repofi^
tory. It contains an account of many fadts
which appear to me curious and important ;
^nd which confirm the obfervations I h^vo

A a 3 made

3s8 SUPPLEMENT,

made in the firft and fourth ESkys in this
Tre^tife.r— Some of iktfc fzQ;s I wiU hero
beg leave to recite«

In the firft EiTay I have aflerted, tlut there
is a much greater difference between the pro--
babilities of life in great towns and in country
farifces^ than is commonly fufpeded \ aQd» a$
one proof of this^ I have obferved, that tho*
ii> London the greateft part of the natives die
under three years of age^ ip the country the
greater part live to marry. Mr. Muref% Ob<r
fervations and Tables give a diftindt demon-?
ilration of this, by fliewing, that in the pro-
vince of Vaud^ the greater part of the inha-^
bitants live many years beypnd the age of
maturity. — ^But to be a little more explicit.

The diftridt of Voud^ in Switzerland^ ct>n-5
tains I i2>95i inhabitants of all ages; z^^'jj'f^
families*^ 3^>32S married perfons; and vt^
annual medium oi births y for lo years before
1766, had been 3155 5 oi weddings ^ 8081 of
deaths^ 2504.— -It appears^ therefore, that
the married are very nearly a third part of
the inhabitants, that the number of perfons
to a family is 4!; and that one in 45 of the
inhabitants die annually. It n>ay be further
learnt, by dividing half the number of the
married, by the annual medium of vired-?
dings, that the expectation of marriage in this
country ift 23 years and f ; and, from the
proportions of the births^ weddings, and

deaths

SUPPLEMENT. 359

ti^aths (a), that the greater part of thofe
who are born live to marry. But of this fa<ft
there is, I have jufl intimated, a more par-
ticular and difl:in(ft proof.— From a Table
given by Mr. Muret^ of the rate of human
mcM-tality in this country, derived from re-
gifters kept in 43 parifhes, of the ages at
which the inhabitants die, it appears, that
one balfoi all that are born live beyond 41
^ears of age.-^The examination of this Ta«
ble will, undoubtedly, be a gratification to
the reader i and, therefore, I have chofen to
make it a part of thefe additions. I have
alfo here given the Table referred to, in p. 1 94
and 268, of the probabilities of life in the
parifli of Hofy-Crofsf near Sbrev)Jbury \ and a
/i6/r^ Table, which! have formed from a re-
gifter in Sufmilchis works, of the ages at which
the inhabitants of a country parifli in Bran*
1>ENBURGH died, during 50 years; or from
1710 to 1759. — I have further thought pro-
per to add, as contrails to thefe Tables, two
Tables exhibiting the probabilities of life at
Vienna and Berlin. — ^The following ob-
fervations concerning thefe Tables fhould be
attended to.

The Table for the country of Vaud, tho*
it gives the probabilities of life in its firfl:
ftages very high ; and, at fome ages, more
than double to the probabilities of life in
great cities; yet, certainly, gives them too

{a) See the note, p. 196, &c.

A a 4 low.

36o SUPPLEMENT,

low. For, firfty it has juft appeared, that h\
this country the births exceed confiderablj
the deaths. The emigrationS| like wife, from
it are very numerous, as will be prefently ob-
ferved 2 And the neceffary effed: of thef? two.
caufes is, to make the regifters give the num-
ber of deaths in the firft ftages of life, too
great in comparifon of the deaths in the laft
ilages. A Table formed from fuch regifters
mufl: give the probabilities of life too low^
according to the obfervations in the 4th EfTay ;
and, in the prefent cafe, they muil be given
fo much too low, as to afford fufHcient rca*
ion for concluding, that the greater part of
the births don't become extinct 'till near the
decline of life.

After 40, the probabilities of life in this
country decreafe vecy faft ; and in old age,
they appear to be lower than the probabili-
ties of life in great towns. I have afligned
the reafon of this fadt in page 270, &c. All
turned of 65 or 70 in greisit towns, are a fe-
le£ced body confifting of perfons feafoned to
their iituation, and poiTefrcd of conftitutions
particularly ftrong ; and they may, I think,
be not improperly compared to a company of
perfons on a hazardous journey, who are be-
come a fet of picked and hardy travellers, in
confequence of having loft all the tender ani
infirm, and been ufed to inclement \yeathcr
and fatigue. •«^— Perfons o^- feeble frames may,
with the help of the iimple manners ana

pure,

SUPPLEMENT. 361

pure air of the country, attain to old age ;
bttt in great towns they fland no chance for
this ; the efFed of ^yhich muft be that, at
the fame time that greater numbers will at-
tain to old age in the country, they will die
ofFfafter. Thus 5 in the diftrid of Vaud,
the numbers alive at y^ are above double the
numbers alive at the fame age at Berlin ;
but thofe who attain to that age at Berlin^
have a greater expeSiation of life. The fame
may be obferved of Northampton comr
pared with Vienna and London.— Infhort;
the truth is, however ftrange it may feem»
f^ that the deftrudiye influence of great towns
<* on life is the very reafon why old people
^' live longer in thezn, than in fmall towns
<* and in the couqtry."— Mr. Muret has ta-
ken notice of this fad ; but, fuppofing it not
genera], he afcribes it to the particular pre-
valency of drunkennefs in his country. He
had, he fays, orice the curiofity to examine
the regift^r of deaths in one town, and to
mark thofe whofe deaths might be imputed
to drunkennefs, and he found the number fo
great, as to incline him to believe, that hard
drinking kills more of mankind than pleu-
nfies and fevers, and all the moft malignant
diftempers. This, probably, is very truei
but the fa(A I am coniidering is not owing to
it. Drunkennefs cannot be fuppofed to pre-
vail more in the country than in great towns.
And it always deftroys long before old age.
7 The

362 SUPPLEMENT;

The obfervations now made aie applica^
ble to the Table for the country pariih in
Brandenburgh ; for it appears from Sufmiicb*%
account^ that the births there exceed the
deaths more than in the country of Vauo ;
nor is it to be imagined^ that there are not
likewife many emigrations from it, particu-*
larlyj to Berlin and the King of Prujia'^
armies.

From the Tables for ViEMNAandLoNDON»
compared with the Table for Berlin, it ap-
pears that the lafl: of thefc towns, tho' much
the fmalleft, has at fome ages even a worfe
effeA on the duration of life than eithec of
the former : And the reafon, perhaps, may
bs, that the inhabitants there are much more
crouded together. Sec p. 225, — ^Between
the ages of 30 and 35, and tilfo bttween 42
and 52, there is an irregularity in the Ber-
lin Table, which, very probably, would not
have appeared in it, had it been formed from
the bills for a longer term of years. — ^The
like obfervation might be made on an irre-
gularity in the 2d Table, between the agesi
of 25 and 30.

From the age of 25 to 45, Vienna ap-?
pears, in the Tables, to be lefs unfavourable
to life than London ; but it cannot be d&?
pcnded upon that this is the truth, for the
Vienna Table may give the probabilities of
life at tbefe ages higher, qfixly becaufe the re*
cruits from the country come to it later, or in

greater

SUPPLEMENT. 365

greater numbers/ after 30 and 40^ than in
LoNPov. A like efFe^ would alfo arife
from a greater number of migrations in old
age from London than from Vienna. See
the note, p.

In forming the Tables for Vienna and
Berlin, I have applied the corredion ex-
]>lained in the 4tfa EfTay, and demonftrated
there to be necefiary ; and, in making this
irorredtion, I have fuppofed, agreeably to the
proportion of the births to the burials, that
a iiith of all who die in thefe cities, are per^-
fons who removed to them at 20 years of
ftge.— !»NotwithAanding this correction, the
Table for Berlin gives the probabilities of
life between 1 o and 20 fo high, and in fuch
difproportipn to the probabilities of life im-
piediately after 20, as to exceed all the bounds
pf credibility. The true reafon of this may
be learnt from what has been faid in p. 225,
pf the rapid increafe of Berlin.

My chief purpofe in giving thefe Tables
is to exhibit, in the moft flriking light, the
difference between the flate and duration of
human life, in great cities and in the country.
It is not pofiible to make the comparifon^
without concern and furprize. I will here;
beg leave to lay it in one view before the
reader, deiiring him to take with him this
confideration, that, for the reaibns I have
explained, it can be erroneous only by giving
the difference {a) much too little.

{a) See p. 222, &c. p. 252, p. 246.

Pro-

564 S U P P L E ME N T^

proportion of Inhabitants dytng annually in

P»iiDe

Viud

11045

Cenwtry Panfli

in Brandenburg

I 10 45

Holy-Crofs

near
Shrcwibury

I in 33

London

I in 20|

Vienot

4 '» ■

I inip^ji iq%67

(4

il ' lw . ' .

Ages to which half the born live*

PaiiDe
Vaud

41

Country Pari/h
in Brandenburg

Holy-Crafi

%Midon

▼knn

25t

27

H

2

Bedh.

Proportion of the Inhabitants (^) who reach

80 years of Age.

Pai&De
Vaud

T

1 inzi-s

Country Parilliy

Brandenburgh

Ho]y- Croft

London

Vienna

I in 22t

I in i I

1 in 40

I in 41

BerHa.

»in37

^«pi

The

(a) S<e page 225. This proportion, were there either
no increafe, or but a low increafe at Bbrlin, would
certainly be found to be much the fame with that in Vi«
£NNA and London.

(b) It (hoald be recollected here, that a confiderable
part of thofe who die turned of 80 years of age in great
towns, are emigrants from the country, whd came to them
in fi^ll maturity, after efcaping the weaknefs of infancy.
And that alfo in general thefe emigrants confift of the.
ipore hearty and robuft part of the kingdom. On both

ihcC?

SUPPLEMENT.
,The (a) Probabilities of liviog one Year

365

O^ds

Ac birth
Age la

. 25
.30

60

PaiiDe
Valid

70
8o|

Af toi
too to 1
117 to I

1 1 1 to I
83 to I
49toi
21 to 1
gXtoi
4C0 1

Cooatry Pariili
Brandenborgh

si to 1

112 to I

110 to I

107 to 1

78 to 1

50 to I

2$ to 1
11 to I

6to I

*\ Holy-Crofi

London

Vienna

4|toi

2 to I

l-fto 1

144 to I

7Jtoi

84 to 1

100 to 1

56 to 1

66 to I

96 to I

45toi

56 to 1

55 to I

31 to I

36 to i

so to I

24 to 1

27 to 1

26 to 1

18 to 1

19 to 1

16 to I

12 to 1

11 to 1

8 to I

7 to 1

7 to 1

m

Berlin

lito i
[23 to I
50 to I
44 to I
32 to I
30 to I
18 to I

12 to I

7 to I

Expectations of Life.

^u^^^K^^y-^^^

32t years
35f

28

18

»i

7I

4I

London

Viemu

From

thefe accounts the numbers attaining to old age in great
towns oueht to be much greater than in the country. In
London, Vttrmay and Berlin, they ought to be nearly douhh ^
but we fee, that^ in reality, they are fcarcely half*

{a) Thefe probabilities are here given fufficiently near
Ui the prefeot purpofe, and fo as to err on the fide fa-
vourable

366 SUPPLEMENT.

From this comparifon it appears with how
much truth great cities have been called
the graves of mankind. It muft alfo con-
vince all who will confider it^ that» accord*
ing to the obfervation at the end of the 4th
Effay, it is by no means ftridtly proper to
confider our difeafes as the original intention
of nature. They are^ without doubt, in ge-*
neral, our own creation. Were there a coun-*
try, where the inhabitants led lives entirely
natural and virtuous, few of them would die
without meafuring out the whole period of
prefent exigence allotted them ; pain and
diftempers would be unknown among them ;
. and the difmiffion of death would come upon
them like a ileep, in confequence of no other
caufe than gradual and unavoidable decay.-—
Let us then, inftead of charging our Maker
with our miferies, learn more to accuie and
reproach our/elves.

The reafons of the baleful influence of
great towns, as it has been now exhibited,
are plainly,

Pirft, The irregular modes of life, the
luxuries, debaucheries, and pernicious cuf-
toms, which prevail more in towns than in
the country.

«

vourable to towns \ but the manner of forming the Ta-
bles is fuch, that they fometimes give them irregularly,
and always with lefs corrednefs than the txpiBatiom^ or
the fame probabilities for periods of years.

. Secondly,

SUPPLEMENT. 367

Secondly, The foulnefs of the air in towns,
occafioned by uncleanlinefs, fmoak, the per-
^iration and breath of the inhabitants, and^
putrid fteams from drains, church-yards,
kennels, and comnion-fewers. — It is, in par-
ticular, well known that air, fpoiled by
breathing, is rendered fo noxious, as to kill
inftantaneoufly, any animal that is put into
it. There muft be caufes in nature (a) con-
tinually operating, which reftore the air after
being thus fpoiled. But in towns it is, pro-
bably, confumed fader than it can be ade-
quately reftored 5 and the larger the town is,
or the more the inhabitants are crouded to-
gether, the more this inconvenience muft
take place.

But I muft proceed to fome more of Mr.

Murefs obfervations. In the 4th Effay,

p. 271, &c. I have given an account of fe-
veral fads which prove the probabilities of
life to be higher among females than males.
Agreeably to this it appears, that in the dif-

{d) A welUknown and- excellent philofopher has for
fome time been employed in enquiring into thefe caufes }
and he has made feveral curious and important difeove-
ries, of which I hope the world will foon receive a par-
ticular account. One of thefe difcoverics has been
lately publifhed in a pamphlet, entitled, DinQumfor
impregnating Water with fixed Air^ in orier to communie^
t$ it the peculiar Spirit and Virtues of Pyrmont Water ^ and
other Mineral Waters of a Jimikr Nature. By the Rev.

Dr. PXIIBSTLY.

tria

^68 SUPPLEMENT.

trift of Vaud^ half iht females doh'f ditf till
the age of 46 and upwards^ tho' half the
males die under 36. This great difference is
in fome meafure owing to the military aiid
commercial emigrations among the males i
but it appears undeniably, that thtir greater
mortality contributes likewife to it. The
number of males who died, for a courfe of
years, i^ 39 parishes of this diftridt, was 8 1 70 ;
oi females 8 1 67 ; of whom the numbers that
died under one year of age were 1817 maiesi
and I '^o^ females i and under 10 years of agcj
3009 males, and 2 ^()^ females. In the beginning
of life> therefore, and before any emigrations
can take place, the rate of mortality among
males appears to be much greater than among
females : And this is rendered yet more certain,
by the account Mr. Muret gives of the pro-
portions of the deaths among males and fe-
males in the frji year of life at Veve y. In
this town, he acquaints us, that for 20 years
ending in 1764, there died in the firft months
oim^es 135, to %() females \ and^ in the firft

year, 225 to 162. To the fame efFc<ft it

appears, from a Table given by Sufmilcb {a)^
that in Berlin 203 males die in the firfb
month, and but ib^ females \ and in the firfl
year, 489 to 395 ; and alfo, from a Table of
Struyck'Sf that in Holland^ 396 males die
in the firft year, to 306 females.-^Vfh^t i&

{a) Sec Sufmilch*s GgttUche Ordnung^Voh II. p. 317, &c.

moil

Supplement. 369

tnoft of all remarkable is, that thefe accounts
£hcw, that both at Vevey and Berlin the
JiiU-born males are to the jiill-born femalesy
as 30 to 21, or nearly in the proportion given
by the accounts referred to in p. 274.

The whole number of inhabitan^ts at Ve-
vey in 1764, was 3350* Of thefe 1931
were females, and only 1419 males. Sixty-
fix were widowers t and 200 widows. The
number of batchelors^ above i6 years of age,
was 529; and of virgins i above 14 years of
age, 734. See Mr. Muret's Tables, p. 124.

Mr. Deparcieux at Paris, and Mr. JVar^
gentin in Sweden, have obferved, that not
only women live longer than men, but that
married vfomtu live longer ih2in Jingle women*
The rcgifters examined by Mr. Muret con-
firm this ; and it appears particularly, that^
of equal numbers oi Jingle and married vio-'
men between 15 and 25, more of the former
died than of the latter, in the proportion oF
ii to I . The reafon of this may be, as Mr.
Muret acknowledges, that the women who
piarry, are a feleded body, confiding of the
more healthy and vigorous part of the fex*
But this, probably, is by no means the only
reafon ; for it may, I think, be expedled,
that in this, as well as in all other inflances^
th.e confequences of fqllowing nature muft
be favourable.

The fads recited here, and at the end of
the 4th Eflay, prove, beyond-the poffibility of

B b denial^

370 SUPPLEMENT.

denial {a)^ that there is a difFerencc between
the mortality of males and females. — ^^I muft
however obferve, that it may be doubted,
whether this difference, fo unfavourable to
males, is natural; and the following fadts will
prove, that I have reafon for fuch a doubt.

It appears, from feveral regifters in Su/^
m/c/js works, that this difference is much
leis in the country pariJJoes and villages of
Bkandenburgh, xhzn m tht towns : And,
agreeably to this, it appears likewife, from
the accounts of the fame curious writer, that
the number of males in the country comes
much nearer to the number of females.

In 1056 (m^Wvillnges in Bkandenburgh^
the males znA females y in 1748, were 106,2349
and 107,540, or to one another as 100 to
loi-f. In twenty fmall towns they were95449
and 10,333; or^as 100 to io8i. IuBbrlin
they were, exclufive of the garrifon, 39,116
and 45938 > or as 100 to 117!.

At the time the accounts, mentioned In
p. 206, were taken of the inhabitants in the

{a) In the printed Account of the Society in Nicolas^
Lam^ for Equitable AJfurances on Lives and Survivorjhips^
there is a Table of the values of aiTurances on female
lives y which fuppofes them to be more hazardous than
male lives. This Table is derived from an opinion ge-
nerally received at the time it was compofed \ but I am
deftred to inform the public, that no fuch Table (hall
be admitted into the future editions of that Account;
the fociety being determined to maintain the juft credit
it has acquired, by keeping (Iridiy, in every inftance,
to calculations, founded on the beft obfervations.

pro-

S V PPL E M E NT. 371

Jirbvincc of New Jersey in America, they
were diiiinguiQied particularly into ma/es and
fimales under ai:id above 1 6.

In 1738, the number of

Males under 16 was, 10639. Females 9700
Males above 16 -i^--^:^ 1 163 1. Females 10725

In 17455 thefe numbers were,-

Males under 16 — 14523. Females 13754
Mates above 16 — ^ 1508^. Females 13704

The inference from thefe fafts is very ob-
vious. They feem to fhew fufficiently, that
human life in males is more brittle than in
females^ only in confequence of adventitious
caufes, or of fome particular debility^ that
takes place in poliuied and l-uxurious fo-
cieties^ and efpecially in great towns {a).

From the proportion of the births, to the
deaths m the diftri£l of Vaud, as mentioned
in p* 358, it follows, by the rule in the note
p. s2o8, that the inhabitants ought to double

their

- {a) The number of deaths for^d yenrs at Vbvey, in
the four winter months, (Decemberj January, February
and March) were to the deaths in the four fumnur
months (June, July, AugUft, and September) as 2x40
to 1697, ^^ 5^^ 4- (^^^ ^^' MuteC^ Tables^ p. lOo),
In London and at Pari^, this proportion is nearly the:
feme. At EftlNBtHiGH, as 4 to 3. In 25 country
towns and parifhes mentioned by Dr. Short [New Olfer*
vatUm^ p. 142) as 50 to 4i.«-«The fick admitted into the
H^iel Ditk 2X Parii^ ioT 40 year«, fign 17^4 to 176^

B b ^ were^

37« SUPPLEMENT.

their own number in 1 20 years. But the
fadt IS, that fo many migrate into foreign!
armies and with commercial views, that their
increafe is fcarcely fenfible. Mr. Muret^
after obferving this, enters into a general ac-
count of the caufes which obftrudt popula-
tion in his country. Among thefe he infifts
particularly on Luxury and the Engros-
siNO OF Farms. I wifh his obfervations
' on thefe fubjedts were not applicable to the

prefent Aate of this kingdom : But, perhaps^
there is no kingdom in the world to which
tbey arc fo applicable.— In confequence of
the eafy communication lately created, be-
tween the different parts of the kingdom,
the London fafhions and manners, and plea-
fures, have been propagated every where ^
and almoft: every diflant town and village
now vies with the capital in all kinds of ex-
penfive diflipation and amufement. This
enervates and debilitates i and, together with
our taxes, raifes every where {a) the price of

the

were, in the former months, 314,824; in the latter,
238,522, or as 4 to 3* See Rjchirche'sfttr la P^pukuiw^
&c. per M. Miffanciy p. 18 1. And agreeablv to all this.
Dr. Percival informs me, that at Manchejier the mortality
oi winter ^nA fummer arc to one another as 11 to 8. — It
is remarkable that the births alfo in winter to thofe in
fummer are at V£V£Y as 5 to 4 ; in London as 8 to 7 ^
in the country towns and parishes juft mentioned, as' 7
ft) 6.

*

{a) The price of corn, in particular, has for feme
\^ time been complained of by the poor a$ upprrffiveiy high*

• though

SUPPLEMENT. 373

the means of fubfiflence» checks marriage,
and brings on poverty, dependance, and ve*
nality.— With refped-, particularly, to the
cuftom of engr offing far ms^ Mr. Muret ob-
ferves, with the higheft reafon, that a large
tra£t of land, in the hands of one man, doe$
not yield fo great a return, as when in the
hands of fcveral, nor does it employ fo many
people; and, as a proof of this, he mentions
two pari(bfs in the diftridt of Vaud, one of
which (once a little village) having been
bought by fomc rich men, was funk into a
iingle demtfne \ and the other, (once a lingle
demefne) having fallen into the hands of fome
peafants, was become, a little village.— How
many fads of the former kind can this coun-
try now furnifh ? — And there is reafon to
apprehend they will go on increafing.— The
euftom of engroffing farms cafes landlords of
the trouble attending the neceflities of little
tenants and the repairs of cottages.— > A great
farmer, by having it more in his poorer to
fpeculate and to command the markets, and
by drawing to himfelf the profits which would
have fupported feveral farmers, is capable,
with lefs culture, of paying a higher rent.

though far from being fo high as it generally was at the
en4 of the laft century. This is a ftriking fa£t wl#ch
implies that *the hvoer part of the nation are now morp
diftrefled than ever. 1 he confequence has been a re-
duction of their number ; and this is an effeA that mud
|o on increafing, with increafing luxury and taxes.

Bb3

Ous

I

374 SUPPLEMENT.

Our fupcriors, therefore, find their account
in this evil .-T— But it is, indeed, erefting^r/-^
n)ate benefit on public calamity; and, for the
fake of a temporary advantage, giving up the

nation to depopulation and diftrefs.^ We

have, for many years, been feeling the truti
of this obfervation.

Dr. Davenanf^ (the beft of all political
writers), tells us, that at Michaelmas, in the
vear i^^5, it appeared by a fu|vey of the
nearth-books {a) that the number of houfes
in all England and Wales was 1,300,000,
pf which 554,631 were houfes of only one *
chimney. See Dr. Z)^w^»/7»/'s Works, Vol. IL
p, 203 .»rr-In his ^ffay on Woy^ and Means, &c.
Vol. I. p. 33, he gives a particukr account
-pf the number of houfes in every county,
atcordiqg to the hearth^books of Lady«*day^
1690 J and the funa total then was 1,319,215.
r-*-At the rejioration it appeared by the fame
hear th<- books, that the number of houfes ill
^he kingdom (^), was i,230,ooo.--rln the

{a) At this tiipe tberp was a Xzx of two (hillings on e?eiy
6rt'heanh\ which was taken off at the Revolution,
^ecaufe reckoned ** not only a great opprcflioft to the
** poorer fort, but a badge of flavery on the whole pco-
f* pic, expofing every man's houfe to be entered into
** and fearcbed at pleafure by perfons unknown to him."
PttamhU to the aSf for taking awoy the rtvenue arifing bj
^earth-mmey, % Wiliiam and Mary, Chap/io.

(k) Continuation of if*/>/», Vol. I. p. 53.

intcrYa!,

SUPPLEMENT. 375

iotervaU therefore, between the r^Jioration
and the revoJutidn^ the people oFEnglanp
bad increafed above 300,000 ^ and " of
^VsMALLER TENEiviENTS, Dr. Davenant
'* obferves {a)^ there had been, from 1666 to
'* .1688, about 70,000 new foundations laid."
*— But what a melancholy reverfe has taken
place fince ?— In 1759 the number of hoiifes
ia ENGLAND' and Wales was 986,48;2 ;
of which not more than 330,000 were houfes
having Icfs than fcven windows ; and 282,429
were cottages not charged on account of po-
verty.— In 1766, notwithftanding the in-
creafe of buildings in London, the number
icS houfes was reduced to 980,692 {b) ; of
which ^76,149 were cottages not charged.
According to tbefe accounts then, our peo-
ple have, fince the year 1690, decreafed

near

{a) Dr# Dav<nant*s Works, Vol. I. p. 370.

{b) See Confideratiom on tht Trade and Finances of tits
Kingdom^ p. 95, 97, 98. Printed for fVilkiej 1766. Seealfo
p. 184, &c. of this Treatife ; and my^ Appeal to the Public
^n the SubjeSf of the National Dekf^ p. 86, &c.— It defervcs
particular notice, with refpedl to the accounts here given
of the number of houfes in 1759 and 1766, that, being
returns made by the furveyors of the houfe and window-
duties throughout all EncIand and Wales, they are
fubje£t to no fuch deficiencies as thofe in the account of
the number of houfes in London, taken by Mr. Maii'
land from the pari/h books, and mentioned in the note,
p. 182. — The reafon is, that no landlord or tenant can
ever coofcnt that any two or more houfes belonging to him,
fliouM be charged by the aiTefTors of the window-tax as

B b 4 y ftngle

376 SUPPLEMENT^

near a tnillion and a half^ — ^And the waft«
has fallen principally on the inhabitant cxf
cottages ; nor indeed could it fall any where
ipore unhappily ; for, from cottages ouf
navies and armies are fuppUed^ and the
lower people are the chief ftrength and fe^
curity of every (late,— What renders this ca-
lamity more alarming i;5» that the inhabit
tants of the cottages thrown down in the
country, fly to London and other towns,
there to be corrupted and perifh (/j),r— I know
I (ball be here told that the Revenue thrives.
But this is not a circum(tance from which any
encouragement can be drfiwii. It thrives, by

9, caufe
•

Jitigle houfes ; becaufc, in this cafe, he would be taxe^
tpo high, and pay more than the law required, — —For
inftance. A building having 20 windows, divided into
two di{lin6i tenements, with a family in each, if charge^
^s a Jingle houfe, would pay, befides 3 1. for the houfe,
15. yd, for every window, or t /. 131, jod, in all :
whereas, if reckoned what it really was, two contiguous
)ipufes, it wpuJd pay, fuppofmg 10 windows in each
tenement, 6 s. to the houfc duty, and only 10 d, for each
"window, or iL 2s. Sd, in all.-r-The number of houfes,
iherefore, fuhje<^ to thp houfe and window-duty, givea
in the above returns, niufl probably be the full number
of fuch hopfes in the kipgdoip.

■

{a) Dr, Daveftant fays, from Mr, Kln^^s Obfervations,
" that the fuppl^y of LoNpuN alone takes \ip above ha^
*' the neat ipcreafc of the kingdom." — Is it then to be
wondered at, that the fupply of the wade in all the towns
wf the kingdom, added (o that Increafe of luxury and
laxes, and of the drain to our armi^s^ and nnvies^ zndfonigu
&tilem£7fts, which has taken place within thefe 70 ycar^
jl)ouki have fo far excc^ed the increafft of the Kingdom^

SUPPLEMENT- 377.

ft ctafe that is likely in time to deftroy both
itM£ and the kingdom ; I mean, by an in-^
creafe of luxury , producing fuch an increafe
of confumption and importation (tf), as fc-
xrctly accelerates ruin, while at prefent (as far
a« the Revenue is concerned) it overbalances
the effeds: of depopulation.— *—^ What reme-
dies can be applied in fuch circumftances ?*^
This is a queAion of great importance^ which
requires a more deep and careful difcuflioa

as to produce the depopulation I have mentioned ?— It
>as be^n aflerted by political calculators, that no popu-
lation can bear more than one foldicr for every hundred
fouls. This (s faying a great deal too much ; but were it
true,, the number of our foldiers and failors, even in
fface^ would alone be fufficient to reduce us to nothing
in a little time.

A flouriibing commerce, tho' favourable to population
in f^me refpe&, is, I think, on the whole, extremely
unfavourable s and, while it flatters, may be dcflroying t
particularly, by jncreafing luxury, the word enemy of
population as well as of public virtue ; and by calling
ofF too many perfofts from agriculture to unhealthy
trades and the fea-fervicc.-*-Suppofe 50,000 failors, ad-
fled to other burdens, to have been formerly the whole
number the nation could bear without decreafing. In
fuch circumftanceSft it is plain, that any caufes which
^oqbled or tripled that number, would depopulate with
j-apidity.

{a) For Example. In Londok, thofe who ufed to
fatisfy themfelves with one houfe, or perhaps ^tf/^ahoufe,
inuft now have two houfes. Thofe who u(ed to live
plain muft now live high ; and thofe who ufed to vfatky
muft now be carried. This is the reafon of the increafo
of confumption and of buildings in London, and not an
increafe of the inhabitants, for the number of inhabitants
is certainly I^fs now than it was forty years ago. Vid.
page 190*

than

378 SUPPLEMENT.

thai I am capable of giving it. I will, there-^
fore, ooly anfwer generally and briifiy in t
ftjrle and language fimilar to Mr. Muref^

Enter immediately into a deciiive enquiry
into the flate of population in the kingdom.— ^
Promote agri€ulture.-*-*-Drive baoc the.inha«-
bitants of towns into the country.— r-Eftabliih
Ibme regulations for preferving the lives of
infants. — Difcourage luxury^ and celibacy,
and the ingroffing of farms. — Let there be
entire liberty ; and maintain public peace by
a government founded not in confiraint, but
in the refpe^ and the hearts of the pQople.«~
But above all things, if it be not now too
late ; " find out means of avoiding the mife*
f^ ries of an impending bankruptcy, and of
f^ eafing the nation of that burden of debts
•• and taxes under which it is finking.'*

P O S Tr

SUPPLEMENT. 379

POSTSCRIPT.

C^ntammg an Account <^ the Influence of th
different States of em'/ Society on P^pda^
fion ; of the Policy of former Times witb
reJpeSt to Jnclofures^ engrojjing of Farms^
and the Encouragement of Agriculture ; and
flfo of the State of the lower Clajfes ofM^^
formerly^ gompare({ with (heir Statg (^
prejent^

THE following obfervations and faft«
have lately occurred to me in recon-
fiderihg the prefent ftate of population in
this kingdom 5 and as, perhaps, they arc oi
foma importance, I (hall beg leave to in«
froduce them in this place.

One of the moft obvious divifions of the
Aate of mankind is, into the wild and the
fivilized ftate. In the former, man is a
creature rude, ignorant, and favage ; running
about in the woods ; and living by hunting,
or on the fpontaneous produdions of the
eartlu In this ftate, the means of fubfiftence
being fcarce, and a large quantity of ground
neceflary to fupport a few, there can never
be any confiderable increafe. — In the latter
jflate^ man is a creature fixed on one fpot,

4 •. employ-

380 S U P P L E M E N T;

employing himfelf in cultivating the ground^
and enjoying the advantages of fcience, arts,
and civil government. Of this laft ftatd
there are many different degrees or ftages,
from the moft fimple to the moft refined and
luxurious. The firft or the fimpIe flages of
civilization, are thofe which favour moft the
increafe and the happinefs of mankind : For
in thefe flates, agriculture fupplies plenty of
the means of fubfiftence ; the bleflings of a
natural and fimple life are enjoyed; pro-
perty is equally divided ; the wants of men
are fe^, and foon fatisfied ; and families arc

cafily provided for, On the contrary. In

the refined ftates of civilization property is
engrofled, and the natural equality of men
fubverted ; artificial necefiTaries without num-
ber are created ; great towns propagate con-
tagion and licentioufnefs ; luxury and vice
prevail I and, together with them^ diieafe,
poverty, venality, and opprcffion. And there
is a limit at which, when the corruptions of
civil fociety arrive, all liberty, virtue, and
happinefs oiuft be loft, and connplcte ruin
follow.— -Our American colonies are at pre-
fent, for the moft part, in the firft and the
happieft of the ftates I have defcribcd ; and
they afibrd a very ftriking proof of the effects
of the different ftages of civilization on po-
pulation. In the inland parts of North-
America, or the back fettlements, where
the modes of Jiving are moft fimple, and al-

4 moft

SUPPLEMENT. 381

inofl every one occupies land for himfelf^
there is an increafe fo rapid as to have hard*«-
ly any parallel. Along the fea-coaft, where
trade has begun to introduce refinement and
luxury, the inhabitants increafe more flowly :
And in the maritime towns (if I may judge
from the bills of mortality at Boston, men-'
tioned in page 200) they do not increaie at
all {a).

' fiut to confine my thoughts to my oirn
coutitry. — Here> it is too evident that we are
far advanced into that laft and worft ftate of
ibciety, in which falfe refinement and lux-
ury multiply wants, and debauch, enflave^
and depopulate. — Among the evils of this
ftate, and the caufes of depopulation, I have
mentioned the accumulation of property. As
this is an evil which has been for.fome time
increafing among us, I will give a brief ac-
count of its tendencies and effeds, with a
view, particularly, to the prefent circum*
ftances of this kingdom, and to fome ob;**
je^tions which have been ftaited.

By the laws of Lidm'us, no Roman was to
hold more than hvcn Jugera of land. ** Only
** revive, fays Mr. Sufmilcb^ this law, or
f* that of Romulus 9 which limited every Ro-
man to two jugerdf and you will fooa

€€

{a) Along the fea-coaft they double their own num-
ber in about 25 years ; but in the back*fettlement8, in
1 c years. See kjptf L page 206 ; and A Difcowrfe on
Chrtfiian JJmon^ by Dr. Styles, p. 109.

♦^ convert

3?2 S U P P L E Me N. t*

'^ convert a barren defart into « imfy znd
^* crouded hive/'-— The doubts of fome in*
genious men on this fubjedt^ have^ indeed^
greatly furprixed me. I can fcarcely think
of a more evident maxfiEn, than that '* the
^* divifion of property promotes population/*
—Let a trad: of groiuid be fiippo^ed in the
hands of a multitude of Uttie proprietors and
tenants, who maintain themfelves and fami-^
liA by the prodnce of the ground they OC'^
cupy, by (heep kept cm a common, by pouI-»
try, hogs, &c.; and vrho, therefore, have
little oacalion to purchafe any nf the means
of fubiiftence. If this land gets into the
hands of a few great farnxers^ the conie-*
qoence muft be, that the little farmers will
be converted into a body of men who earn
their fubfiflence by working for others^ and
who 'will be under a neceflity of going to
market for all they want. And, fubiiilence
in this way being difficult, families of chiU
dren will become burdens, marriage will be
avoided, and population will decline."- ■ ■
At the fame time there will, perhaps, be
more labour^ becaufe there will be more
compulfion to it. More bread will be con^
fumed, and, therefore, more corn grown ;
becaufe there will be'leis ability of going to
the price of other food. Parifhes, likewife^
will be more loaded, becaufe the number of
poor will be greater. And towns and ma-
aiufaifiures wUl incrcafc, becaufe more will

bd

SUPPLEMENT. 383

bt driven to them in queft of places and
employments.— This is the w>y in which
the engroffing of farms naturally operates :
AnA this* is the way in which, for many
years, it has been adually operating in this
kingdom.

It deferves particular notice, that the ob^
fervations now fuggefted (hew, that the very
caufes which produce depopulation aniong
us, may, for fome time, promote tillage $
and I will take this opportunity to add, that
they will alfo account for the following
fa€t.— In the year 1697, wheat was at 3/.
a quarter, and other grain proportionabl/ .
dear. But there was no clamour, and die
exportation went on. See a valuable and
ufeful Pamphlet, entitled, 7'Aree TraSfs §m
the Corn Trade, page 100, 107, 145. At
prefent, though the quantity of money in
the kingdom is doubled, when wheat is at
2 /. 8 s. a quarter, and in general before any
grain, except oats, gets above the prices at
which the law allows a bounty on exporta*
tion, there is an alarm, the poor are ftarv-
ing, infurredtions begin, and the exportation
is prohibited. — I referred to this fa6t in the
note, p. 372 ; and the true reafon of it feem^
to be, that the high price of bread was not,
at the time I have mentioned, of eiientiai
confequence to the lower people, becaufe
they could live more upon other food which
was then cheapo and becaufe a]fo being

more

3S4 S U P P L E M E N Ti

tnore generally occupiers of land, they wertf
lefs under a nepeflity of purchafing breads
Whereas now, being forced by greater dif-
ficulties, and the high price of all other
food, to live principally or folely on breads
if that is not cheap, they are rendered inca*^
pable of maintaining themfelves.

In confirmation of this account, I will beg
Iqave to mention, that, though during the
whole laft century^ corn (wheat, ryc« oats^
and barley) was generally dearer than it bas
been, at an average^ for the lad 40 year& 1
yet flelh-meat was about half its prefent'
price : And thatj in an ASl of Failiament of
the 25th of Henry VIIL beef, veal, pork^
and mutton are mentioned as the food of the
poor, and their price limited to about a halfr
penny a pound. See Mr. Hume's Hiftory of
the iudors^ Vol. II. page 285. Beef and
pork, in particular, were fold in London
at two pounds and a half, and three pounds
for a penny 1 at the fame time that wheat
was at 7^. and &/• a quarter {a)^ and bore

the

{a) Even fo far back as the year 1463, the price of
Di^ heat was reckoned not .too high at 6x. 8^. per. quar-
ter ; nor that of barley at 35. and rye ac 4^. ; for it was
in that y^ar enaded, that the importat'iGn of thefe three
forts of grain fhould not be allowed till they got above
thefe prices. See Mr. JnderfirCs Chronological Dedulfim
tfCmnmnu^ Vol. I. page 280.

By a Sutute of % Pkilip and Mary^ '553^ I^^ve was
given to export thefe three kinds 0/ grain tiU th^y rofe
to thefe pritei. Ip^ p. 387.

'. J5 U p. P l!e M E it T: ^ 385

ine 'fame prdp6rtioti to the price of EcQi as
it would bear now, .wcpc it at jibout 4 /. a

quarter.

BjF'aA dfflinahcte in 1563, the exportation prices wcrtf
nxed to 10 s. per quarter for wheat ; 8 s* for rye^ peafe,
and ^^<7fff ; and 6i. Si*, for ^i^/.t— Aiid ill 1593, to 1 /.
fof fvbeat ; 13 f. 4 i. pea/e and ^r^TTU ; and 12 i. ^or/Qf and
^ntfiif/ lb. p. 401 and 442.

Ih

P R, I c K.« per Q^ir art B/ii

6fWiie<t. Of Malt.

' /• s, d, L s. dm
H914 o 14 8— -^0 0-
1494, 6 4 o— ^ — o o o-

bfOati;
/. s* a,

o 00 6

*S04> 0' 5 8
1512, 062-
1521^ I o o-

■^o •00 d
*o 00 6

026

Froin 1553 to ^— 1556, 080

BefofiB ,harve{(, in 1557, 2 13*4
After barveft, to 1557, 0*80

1560, 080

Before hirveft, in 1574, 2 16 6-^— ^-o 6 o
After fiaweft, in 1574, i 4 ,0 ..o o jc>

'587* 3 4rO— — o o-

■<yo o-
-040
^o 0-: — c 00 (>
-o 5 o— — 60 o
% 4 o— — So 00

O 5 ©■:—'—« 10 o

o 5 o— — 6 5 6

o 00' O
o 00*0

o oa*6
06 6

A<icarthoccaflon- 1594, 2* i>6 o — -^o 00

!firi "?'& '595. 2^1? 4-— t o 0—0 00 o
exportation ;oc»> »^.«'^ •

inisg6bygreat ^59^» 4 o o 1 6 8

raips 1597^ S 4 o~— t 6

Average PrIce,
i^rbfh 1606 to — : 1766, i \i 6-~-i 2 6
F«>m 170710 -i- 15^5; 1 12 6— fc-r-l 19
From 1766 to?—. 1772, 2 '3^6i-i— ^ ^ o— ^-t-o 19 a

ger Bp- #7/^mf^ Cirom^ PM!^,4n^m p. ix^to
p.4»4i A^f^fSr^^ Jri^gfj onthi'G^n Tf^, p. 98, &c.

• C c * With

' 1 *

*

f

^U S IJP'PXl; M ENT.

garter. *Stt^C\biihmiv^n Freli6/km^ p. u6.
k*ap^rs, inde^d^^At our mc^fton took

great

Ik

Wkb^hefe prices of idru kt til «omflu«^ ^ictol of
Jlffij at two -or throe difereAt periods.

In iKiT^ the nfice of Offbeat i^a9 ttotA ^sl Sd» to 6i. 8i£ '
1*11 lVr|^V«. See M RegtAnims and E/tMift>mem tf tt^
Hbujhold of Henry Alger/ion Pircjfy the Jy^ E^rl wf Mr*
tb^berlanJ, at his JCaJlles of fVrefiU and LdtmgfieU in
Yorkjhirij begun Afyio Dem. Hk%) p^t^ ^ 4- Let u»
call the mean price ts.ld* The price of malt was 4>»
and' of oats '2^. We may «dberefore ^ckon, that the
nominal price of gf kid at tbt# tithe wBt about a 'feventb of
its nominal prico for the laft 20 ytara. ,

The price of a fat ox at tiie fame time, and In the
leiliie couiiiy; wtd t$K 4.^/^ of a lean ox, 8j; of a
weather,, is. 8 J ; of a calf, 1 1. 8 4^5 of a hog,^ a s. V^.
f. 5. 6, 7. — The •nominal price of meatf theixfore« was
jio more than about a X5tb of its preltnt prict, aod bore
Ihe fame proportion to the prict of corn that it would
How bear, wei% It M hi^ its prefisnt price.— A lihe ifi*>
#Dreocc oaay* be drawn ftom coaqmamg tbe fol)owin|
prices:

Wheat, in 1^549, was about isx.'oer quatter in L^N*
bOK, Malt, 10 i. ISarley, 9x» Kye, 61. 6 a, Oats,
4 si-i-k ml^ffli ng t)x, , 1 1 1 8 T. A " Weather, 5 y. Ban-
ner, three farthi^^ md, a fenny a -pound. Cheefe^ a half'
fanny a poun4. See Maithma^ Ififtofy of Loodafaa^ ps^

^ In 1574, Ihere was a g^at dearth^ afid wheat was*
befoj% barveft, at a 7. 16 i! oe^ quarter ^ and beef al
Lammas^ fo de^,'^a8'io be fola at twopence- hati^pienny
a pound!"' See Chronieon PretiBfime^ p. 12}. Tlut^is^
beef compared with w^eai^ was at leatt'one mI( cK^plr
than it is now. . • ' . ' . J.

In 144^ wbeat warat 4*1. 6i^ per ^tiaifeK tn XSf^i

Ooatbiiig for a^year, «t the bAf^xiK^^xf ^.cotfmoM

• '

» •

• S It i* 1^ L ETME N t. 3%

^rMt care takeep the pric6 of ile(h low £ii^
the poor; «ind this was pne^of the reafmsof /
the many proclamations publiihed by "Quem
EH%abethy James I. and Charles L againft
tefifi^fle£h in Ltnt and -on fifh dayi^ afi{l .
. ligainft the erediotf of fiew huildings in Lm^
don^ and the zipfidehce la it of the n^ditf
and gentiy.

The*rea£iin now a^gtied liccounts fartlH»if
for the great vswiations m- the price of graia
which u&d to takioi j^laoe formerly; The& -
Ware £tch «$ coiaid liot be now ending ^ hoit^
bread being th^ lefs a hecefikry article of.
fiibfillence, tbef were leTs felt aad rq^a^ed^

* I ha<re Vakea for granted^, in thefe obfcrf
VAtioQSi that .tl>e quantiSty of ground" brought

Tervafit of BufSahflry^ 3^. 4 a. Of a chref carter ana
ihcpHerd^ 45. <?f alyaiHffofhitbantlry^ ^ f. I^/pag^
^iaS^ J099 iho.'^-Cbatkfng^ HtxcMoTt^ at ^Mb ti^lt^ fqeiMi
^ l»ve'lKefl'Cb|a9P9' ia ^omparilbii of the prH;e/of loor^
than even flefh.

' ' Tfie weight of filver coiif pPHkrly^ to the i(rcight <S
filuer Ciaih of the (faame (tentmiliiaiiaii ^wiv^ was fsoili

^ijSi to .ifOlja .ts f>%' IP 27i* K'^^>* *^ *P '54*^ V
6a ^ 4^- ffOfi 155^ i» i6(3iO, as.^ to 60. J^iid
from i6oo to ttte pjrefcnt ttme, as '62 to 6z. But no*
Ubing depends on dtfc ta'ttte^FtfeiK eiiquir^f tbe#li^
}c£l of which is, not the proportion of the fM'ices of the
differqm articles .of fubfifl^nQe imc; to tibe^r jjuicei ^r-
. ^?r^. but tlie j>ro4)ordQn >o 911E AKOTHpa of tK<^r .
jH-ices iftfo^ in g^mparifoii wUli the Tame proporriot) /pr-
|fr^i^. And flals 43fiay be as weil ^ed&ce^ £rqrn the nam"
hai as fcpnal'tha ak/ilute piice*>^TTm5* TTbi price of
bil^act'nc^ii^ if^arj[y 'tl)et^a»e'thst i^^ fOpy^^^^O} *
. Wt, m<0iffamfi^yfitl^ihk price ^f %fg£ and i9uuon> it
% lit lhB#9#'jStf^ cheapen . "

' . . C c i/ • -undctv •

••.1

> ■ " • •• '

«

♦ •

388 SUPPLEMENT- .

HQoer tillage in this kingdom ^ now more
\ than ^ver it was.. This is generally believ-'
'^ ; and, if tnie, the caufes of it have been
' thofe I have mentioned, in cohjyn<ftion with
• the encouragement given to the growth of
« corn by the bounty on exportation, and the
increase of luxury occafioning an increafe of
horfes, and rendering even the poor averfe
to.all bread except that' made of the {a) fineft
ilour. fi.ut, perhaps, the*^fg^ may not be
^ ib certain as fome thinlc iu At lead, .there
is vesSqik to apprehend^that whatever the in-
/creafe of tillage tnight have been *-i'iferfio or
60 years after the Revolutions it is now at
an end.— I have lately received an account
of a large .cdmftion field in Letcf/ier/bire,
which u^d to produce annually 8qo quarters
of com, befides, maintaining ;too cattle; but
whidi how, in cooff quence of being inclo-
sed and getting itito few hands, produces
little or no' corfi ; and maitttflins* nb more
. cattle than before, thqugh the rents are coiv-
fiderably adiKancdd^^-VThis is only . one in-
ftance among mdny of an evil that has been
prevailing for fonfie tim£, and which is the
general e£fed of tl^e law$ ibr incloiing Open

(d) Brtad made of iraHj a&d even af peaji and jwmr,

^•was formerly not uncommon among die lowtr people.

'Bpt no, diftrefies 'could {qi«e Uiem nov^ijb ^t fuch brcaid,

^r etren tolive upon rice^ though the fookl of^a conud6r^'

•We oart 6f the reft oF mankind. ' See^thj EaH! $/ Nor*

ihumfittafuP/ HoufoM Bootx Pjcface, pi 13, Jto. ;

fields.-—

« ■•

(•

«4

SUP PL B MK^TSr T: w^f9

fields.«^ln ^ NtfribampianfixifT/ aixd Jjnct^tr^rt^ h)«
clofiDg^' has greatly prbvailcdV and moft of thfe
new-inclofed iordihips, fa^a ycry fimfibte ifhvter,
^* ^ turned ktta paftur^^ kt conftcfoence tif
*^ which, many loidfliips; baVc not no^ir 56 acr^k
^ pknighed yeartyv in whicty'ifbOy oratl^aft looo
** -were ploughed formerly %isA fcarce an ear of
*' corn is now to be fcen id fomc.chat bore l^imdreds
^ of quarters. — And fo ftverely are the efieAs of
** this felt, that worfe wheat has been lately fold
" in thefe counties on an average, at 7 j^i and
7 1', ^i. the Wincbefier buih^l, for many months
together, than ufed to be fold at 3J. 6^. and
** 4X. And 55-.and 5J; 6^*- has been giren for
•* nS.z chat has *bcen ufualiy bought there at little
•' more than half a crowri.'* Sec a pamphlet,
entitled. An Enguiry into thi Reafom for- aitd againfi
inchjing Open Fields^ by the .Rev. Mr. Addington.
FuUiihed for Mr. Buckiand, Patir-nofter^Row. — '-
In the counties oi Northampton and Leiceftir^ fays
the fame writer,, p. 43, •* the decreafe of the in-
*^ Habitants ii^almoft all the inclofed villages in
•* which they have no cbnfidcrabk manufaftore;
** is obvious to be remarked by every .one who^
** knew their ftate 20 or 3^ years ago, and fees
«* them now, and that to a degree that cannot
♦' but give every true friend to his'country the
•*, moft fenfrble concern. The ruin of former
** dwcHirig-houfcs, barns, ftables, &c. fhew every
•' one who paflfes through rfiem that they were
*^ once better inhabited. A hundred houfes and
families have in fome places, dwindled into
' eight'Or ten. — ^The landholders, in moft parifhes
" that have been inclofed only 15 or 20 years, are
*< very few in comparifon of the numbers who-
^^ occupied them in their . open field iiate. It is*

' ' C c 3 "no

f9€^ SUP PL E M E N T.

• *^. oo uncommon tbin]^ to fee four or five weaTcKf^
'^ graziers engioffi% a large inclofcd lordihip^.
,*^.:whicii was befoce m^he hands o£ 2oor go farnis
** ers» and .a^. many fmaller tenanca or pcoprietorsr.
''f . All their are hereby thrown out of tfapir livings
^ widi theic familiesy and nuniy other families
^ whioh were employed and fupported by-tfaem.-^
JJ.:p. 37; See an account of NcrfolkjAn fome
refpeds fimrlar to this, in my Appeal to ^erPiUfUc
$h the SubjeS of the National Dcbt^ p. pj^.&c. I
can fearcdy think of any thing that (roirid be more
alarming than fuch accounts.— r-How. aftoniihing.
is it that our parliament^ infteadof applying any
remedy to thefe evils., fhould chufe to promote
chenfi, by pafling evevy year, bills, almoil without
number, for new ihblofures ? (a)

'The device, fays Lord Bacon^ (Ejfajy^ civil
and fHoraU Sc6t; 20.) *' 4af King Henry VI L
^* was profound and admirable, in making
^ i^rms and houfes o£ huihandry of a. ftand*

r

(^ I hive hert in view iocIMiires o£ efem faUs ami bpuft
already improved. It is' acknowledged by even the wricera
in defence of incfofares, that thefe diminifh tillage, increafe
rfae monopblies of farms, raife the prices of proviiions, and'
produae ctepopulation. Such* inclofures, therefoie, however
gainful they may be at prefent to a few individuals, are*
tindoubtedly pernicious. — On> the contrary. Jnclofures oC
twajle lands and commons would be ufefol, if divided intp fmall
allotments, and given* up to be- occupied at moderate rents by'
the .poor. But if, befides lefTening the produce of fine wool,
(bey bear hard on the ix>or by depriving, them of a part oE
their fubfiftence, and only go towards increafing farms already
too large, the advantages attending them may not muph ex-
ceed* the difadvantagea.^-Hc that would better Inform himrelf
on this fubjecl, fhould, befides Mr. Addingtpm\ pamphlet'
written againft inclofures, read another written^r t^ero, and •
entitled, l^he Ad^vantagts an4 Difadvantages of inclofi^g Wafit.
hands and Open Fields impart ralljf ftaud tmd cfmfidend. By a.
Country Gentleman.

7 !* ardj.

•CiC

€C

«»

/S'U PEL E M E N T, g^i

ar4;. that h, xxiaiQtain«d.witb fuch 9 pFO-r
poartioa' of H^d to tbem, fts o^ay breed 9
ibbjeA ia (convenient plsnty and 00 fer^
^^ vUe condition^ and to keep th« plough ia
y the hands of the-^5w^^ ap4 not ^iW-*
^* ii'«^/.**— lockxfurep, fays the fa^ne grea|
'^ritery (in his Hiftojy of the ^eign ot Htnry
the Siventb) ^\b^aa ^ tb^t time (or in j 489}
^^ to be more frequant, whereby arable l^nd
^^ was mrn^ ifitq pafture^ which was ^(ily
=*,^ cnapaged by a few berdrmen^^ This bred
**^ a decay of peof^e. In remedying this in-*
^} convenience, the King's wi|[^om ^d^^ho
^/Parliament*? w^s admirable, Inclofures
*^ ti^ey wpuld not forbid > and tUla^^k tjicy
would QQt compi^l I but th^y toQJc a coi)r£i
to take away depopulating incl^mr^4'%vA de^ -
^' p^i^iifg pq^rage b}i CQnfequence. Th^
'^ ordinance was^ that all houfes of hyifban-^
f * dry, with 20 acres of ground to tbcrai;
V (bould be kept up for ever, |oge|Jier jvith
^* a competent proportion of land^tg be qct
*\ cupied with them^and in |io twife to be
*' fevered from them. By thefe means, the
^' houfes being kept up» did, of neceifity,
*^ enforce a dwdler ; and the proportion pf
<' land for pccupation being alfo kept Dp,
*^ did^ of necefHty, enforce that dAveller aot
1* to be a beggar (<a)." The jl^tute here
mentioned was renewed in King Henry ,i\\q
Eighth's time i and every peribo who con-

(tf) Se^ Lord Baicon'^ Works^ V<d. m» p. 431. *

C c 4 verted

4€

4t

%

S9e .6 U P P L E M E ^ T. •

verted tillage into pafture fubjcSed to a fbr^
feiture of half the land^ till the offence wa« •
removed. See ' Mr. Anderfon's Cbronologi-^
eal DeduSlion ^ Commerce ^^ Vol. I. pigc
347.— T — ^In a law of the 25th of the fame
feiga, it is fet forth, '* that many farms, and
** great plenty of cattle, particularly iheep,
^* ha4 been gathered into few hands, where-
^* by the rents of lands had been increafed^
^^*and tillage very much decayed i churches
^' \ind towns pulled down s <he price of pror
** vifions exceflively enhanced^ and a main
♦* irellioifs number of people rendered inca-
^^ pable of maintaining themfelves apd fa-*
miiies ; and, therefore, It was enafted,
that no perfon Ihould keep above 200b
*^* {hee^> nor hold more than two farms f*
Ib.'p, 363. — In the 3d oiEdw. VI. a bill was
brought in for the benefit of the poor, for re-
building decayed farm houfes, and maintain-
ing tillage /igainji too much, tnclq/fng. Parfia-
mentary Hift. yoL III. p. 247. — In the year
1638, there was ^a ipecial commiflion froni
Charles I.- for enforcing the ftatute of ihe
3Pth of EltsiaSetS, l^y which no cottage was '
allowed iri any- couiitry place, without at
leaft four ac/es of .land to it, to prevent th6
increaft of^ the popr, • by fecuring to tiiem? a
maintenance ^ nor were any inmates allowed
in any cottager. to. fecure the full cultivation of
the land, by diffufing the people more oyer it ^
See Rymer*s Fted. 2^, 256. zud 340^-r-By in

r
€€

«•

S tJ P P L E M E N Ti 39 J

A^ inOrdmweirs time,. no new houfe was to
be built within ten miles of LdNi>oKy un]e&
there* werefour acres of land occupied by the
tenant. Parliamentary Hi/i'ory, Vol. XXL'

Such' W-as the policy of former timcs.*^
Modern policy is, indeed, more favourable to
the higher clailes of people ; and the confe-
quence of it may in time prove, that the
whole kingdom will confift of only gentry
tx^A beggdrsy or cS grandees zndjlaves. . i

I -cannot ^ontlude this Poftfcript without
adding dne farther (^fervation which hasT
ftruck me on the prefem fubjeA.-W^ in for-*
^ mer times the numbers of the occupiers of
. land was greater^ "and all had more oppor*
tunities of wt)rking for tbemfehes, it is rca-
fonable to conclude, that the number of
people willing to work for others^ muft have
been fmaller, and 'the* piice of day^iaboaiF
higher. Tins is now the tafe in our Ame^
rican colonics; and this Hkcwife, '.upon, eh*
qviry, I find to have been the cafe in this
coantry formerly.— ^—tThc nominal price of
day-labouF is at prefent no more than about
four times, or at mofl^^&f times higher than
it was ift the yzzv 151*4. But the price of
corn (tf) is^w« times, andbf flefti-mcattind
rftymcnt^about^y^if^w times -higher. See the

{a) Sie Chronietm Pretidfum^ Chap. V. From whence,
xx>mpared;viEitb the account in Chtp. iV« of th< pricerqf
coro • and pthfr commodities. *for ifche kil 600 ye^f?)
siD^ndant evicfence for what 1 have here obfervcd, may
bpcollcftcd; ' ' • '\ ^

• — note.

. . . • ••. • . .
» - • •

^

1 ... ' - •

394. 8 UP P L E M E NT.

note* p. 385.-^80 far, ihtrefore, Ims iho pfio«
of hbouf been from advunping in prpporfioii
to the ixicreafe in tb« cxpence^ of limg*. tbat
it does not appear that it beaf$ novr balf^
proportion to thofe eypeoces that it did for-
nejrly.

Upon the whQle^ Th|e circumftanc.es of ^
lovrer raiilu of men are altered in ftlmoft wt(Pf
refpefi for the worfe, Fronj? littl^ occuputrs
of land» they are reduced t^ the il[ate of da^^n
labourers and bireUngSi and ^ the iaine time
their fubfiilence in xhzt ftate ia become otkore
difficult> in <:onfequence of the caufe juft a£r
figned ; and alfo of iuxury^ which has eis^
tended ita influence even to themv tho' ftarv*
mgi and rendered teoyjim vbeaien breads
andt^ther delicacies^ hecef&ry to thofH^ which
were formerly unk^nown .among them.*«-«T
Sttch a change eannot. but draw afber it imT
portant confequences. It ia theJowerpeoT
pb chiefly that pay. the taxes of a iUtc^ light
its. battles^ carry on its commerce^ and VMm^
tain . its fpleador.* In every ccprntry, >th0
higher ranks arc a Tery/frndl bodj., compar,
ed with. them. £ve4 in this couQtry^ wher«
their numbers are. pcpbably much lefleaed»
they are ftill; more the n^jority th^n is coaw
monly imagined; I for^ .fromv the .retitrat
majde Jby the fttrvey9ra of tiie houfe aiyi.win*
dow-dutiesj itappearg, thatT,ifRSE;«Fair:R.THs
of all the houfeA in the kingdom; are hpufts
not having more thm je'vi^n. \yinp9W4.^, . . ■

»

* . f * « • - • •

.■''■ -/• - .»•

. , * • * . • ^

, • • • >■ .

18 y pp J.» MENr; ^|

Additional Ob-serv

C O^MC'Elt NIN 6

The Schemes of the Societws- for
providing Annuities for Wi4dw^
ftji^ fpr Perfons iii Old Age.

THE following (hort and czfy mettiod
has occurred to mc of trying the fuf-
ficicncy of all ftich ichemes as thcrflxof the
Lo(N&oN .^fvnioir^, and the LnnJadle Socie't'
ties for the benefit of widosvs.

In an adequate icheiDe it can' Inake oa dif^
ference whether the annuities. them&lvea are
paidy or the value of them* in a fidgle pay-^
nlent^ at the tioae they become dtte.**^8up^
pbfe then'a idclety juft eftabhihed* confifting of
6cc> members^ all znafried>men at the age of
40; each of vboto, befides one, pajnticiit 1ft
lUnd^ is'ta Jisfake an annual pay ment.iof five
ghineas.. Suppofe alfo their wiv^s o£ the fam^ .
agQ» .and ^vory widtfw to be^elititkdi on tbt
: .- da^*

5^:6 S^ P P t E M E N T; ^

day her hufbaAd dies, to a life-annuity of 20/.
the firfl: payment to be made at the end of
half ^ year;-^Stippof€ . further, that the ib«»
cicty is to be kept up for ever to 600 mem-
bers, by admitting new ones at the age of
40, as old ones drop off. — In the firft year
(according to Tables HI, IV, ^nd.Y. v^-
pendix) twelve members, at leaft, will die,
and leave twelve widows, each entitled to
20 /. per annum. The valuc; of fuch an an-
nuity to commence at the end of half a year,
the age being 40, is 141 jears purchafe,
by Table III. Appendix^ reckoning intercft
zt.t^.percens. The value, tljcrefore, of 12
fuch annuities ; that is, the whole amount
of the fums becoming^ payable during the
courfe of the firft year, is 3480 /.-—The an-
Aual contribution is 60Q times 5 guineas, dr
3150A and this, together with its intercft
for ibout half a year, or 3.205/. is all that
fuch a fociety could be pofTeifed of to bear
an annual expence of 3480 /.-^It appears^
therefore, that, in order to fupport the ex-
pence of the fuppofed annuities, the annual
contribution of each member ought to hav^
been more, than five guineas.

In a iimilar way it may be proved, that
neither is £dch lan annual contribution ati
adequate fupport to an annuity of ro/. if a
member lives . one yearj 1 5 /. if her lives fwo »
years, and 2i7. if he lives /ir^^^ years, TTiis
^ill appear iifcm the following accouDC*; into

. ' \yhich

SUPPLEMENT.

397

which I have not taken the contributions of
the firft members at the beginnings of the
firft year^ becaufe I fuppofe them fcarcely
fufficient to bear all the expences of manage-
iBent during the whole duration of the ib-
dety: But the firft contributions or pay-
ments in hand» of aU fubfequent members
are included^ thefe being neceflary to render
&e fum of the annual contributions con-
ilantly 3 1 50 /• as the account fuppofes.

I •

*

3260 A

ii .

•» f

■♦ •

J

1

DeduA ijiQi.

Add * g£^2i

Add • 54/.

Sum *, 4864/^
Deduft 2520/.

$t:6oi — Tfafc Stock ofthe ibciofy at the «0j
of the 2d year, being the cootribu^,
tion of 600 ihombcTs acthtvnd of
the jiry? year, together .««& tb< in^
tercft for a jear.

'The value of 12 lile-toaUitJes^ ^
loL each, to 12 wi^ows^ aged 4.1^
left in the courfb nf tht ^ year, at

» The cantributbn of 600 tf taAcni
at die ead of the 2d yeafj ^ethc^
with Its intereft for a year.

-Intereft at 3J of 1550/. for a year.

•Stock at tlie end of three years.
-Value of 12 annuities, 15/. each^

to 12 widows, aged 42^ left in the!

courfe of the 3d year, at 14 yeara

puclufe.

^Contribution, together with its in«
tereft, for the 4th year<

- Intereft of 2344/. for a year.

■ Stock ^t the end of four years.

* Value of 12 annuities of ai/. each^
IP 12 widows, aged 43, 'left the
4th y ear^ at 1 3| years jm^chafe (a. )
Remains 22^2 1 /«

Add - 3 2 60/r — Contributioii, toother witk its in^

- tereft, for tlK*5ni<year.

Adrf - 78/.»^Ihtcreftof222iA'fiirayear.

5559'/. — Stock atthcead otJivejeix%i

^ (n) A fodcty that cl»)re thus ^yftf |he.«itiMf of Jtfce aanin*
lies a); the time chey b«cai9e do^» ioiead pf4ke anftiiiiies'tiMif -
felire9»woold eojoy p^doolar advances i^ {or ImleoanolUbg
would depend oa tl^ ioproveme&t'n.nUdQPt jqo^^i and
time would fooa detertpine whedier' it went on an ajequatc
p|an« .^4-i A ptoof of the fame tiature wilh that here (iftnj

may

Remains 2344/.
Add - 3260/;

Add' - 82/.

^m

Sum - 5686/.
DeduA ^465/.

-••

i

\

f

. S U P P L E M E N r. 399

It muft be obfcrved, that the ftock laft
gifeii> is h& than that immediately precede
ing it ; und that, eoniequently^ in 5 year9>.
the ibciety f^uft begin to run out» and th^
annual contributions appear to be infuffici*-

The firft members will leave much dit
fafa(» number of widows every ^ear, for a

may <»e dediicedl» by oonfidtring tbefe focieties «s bodies
of men united for the purpofe of afluring to one another^
from year to year, annuities for their wi<iows -, and the
>^ay t>f finding the value of fuch ati afTurance ii, to multi-
ply the va^ue df the annuity, by the prc4)abilitT that it Will
become payable in th^courfe of the year*-«>For inftanc^
Let tilt member's age, and alfo his wife's, be 40. Let
the annuity be 20 /. pir ann. for life, or an annuity whofe
Iprdbnt value is, by Tabk VI* (reckoning intereft at 3J
pir ant,) 14 years pvrcbafe; that is, aSdV. The prp^ .
bability t^at a perfon at the age of 40 will die in a yeai^
and that his wife of the fame age will live a year; or, in
x>ther words, the probiibility, that ftich a member wiH
leave a widow in the couife of the ye^r, is, by Tab^ IIL
^p|f multiplied b^ 4^ or .0198. (See p. i&aad 23. 1 '
- j^at is i there will be (he odds of nearly 49 to i, againft
fucli a member leaving a wiHow in the courfe of die yean
The yalfte of the aiuranc^ therdfoi^, h .or98, multt->
fdibd by 280, 9r the 50th part of A 280 ; that^s, 5/. iii.
i— In tne fame manner the vahie of a like afliiranc? for a
year at any other ages laay be eafily calculated. At the
^ ot 359 It4» 5 h^ s At the age of 45, it is 67. 7 k
TMe vau% rhfrefore, SnjQreafes coittinu^lyrwich ige$
aod> if (iven in'an annual payment confbuuly the £amo^
Which is the cafe in thefe focietief, it ought to be greater
fh^*tRe andiuftl paymehf due for 'one year at tbt codi*

fnenet9»t.oMia ^mijnmir. *^ /

, Five ^nefs ffr mmum,. theveft^fCf ^ Jmon/irabi^ ^m •
Infutiicft'iit payment from a tn&rriecj man fgr a lif^'-ar
THiJtyirf<^/.t<rhirwiiigw. -

. , . I . fisw

• • ■

400 SUPPLEMENT.

few of the firft^yfears of the fcheme. Aftef
the fir^ year alfo, the members admitted tp
fupply vacancies, (about 24 annually) will
begin to leave widows ; and, as the whole col^
Jcdivc body ^fuppofed to be kept up to 600)
will be continually growing older, tne deaths
among them, and confequently the number
of .widows left annually^ will be continually
increafing; whereas 1 have fuppofed them
to remain the fame. — This calculation, there-*-
fore, is as favourable as it ought to be ; and
tvery one who will examine it muft be con-
vincedf whether acquainted or not with the
method of mathematically inveftigating the
values of life-annuities depending -oa fur-'
' vivorfhips, that all that the focieties now
. fubfifting promife to widows more than 20 L
or at moft 20 guineas ^^ annum/ f(x an An-
nual contribution of 5 guineas, can have no*
permanent fupport ; and, if paid to prefeni
annuitants, muft be fo much taken away
from ioxxiz future annuitants* And this ap-^
4)ear8 too on the fuppofitions, that there \^-
no difference of age between men and thcif
wives, that nioney is improved perfedly at
compound interefl, and that the probabili-
ties of life among females ar« not higher
than among males.— -How melancholy then
is it to think, of ,the encouragen^ent that has
been given to thefe focieties ?«^ There ars
now in alnioft every jpart of this kingdom,
feme inftitutions or other of.thi^kmd^ J^rm-^

I ed

Supplement; ^or

* * «

hd }XtA as fancy has 4i£tated» without any
knowledge of tfae principles oh which the
values of life-annnitiesr and reve^rfions ought
to be calculated (4). I can, however, with
pleafare^ .acquaint the public; concerning
the two London focietiesi of which I
have taken mote, particular notice^ that, con-
£iting in general of geptlemen of charadler
and fenfe, they have liflened to the infor-
niatioA ttrhich haS been .oBfered them ; &ndy
m confeijtuence of iu either have already, or
probably will foon, refotve on fuch amend-
jnents of their plans as. may render themi
piermanently and effectually the means of the
good intended by them (^)w

I wifii

(tfj There is a fociety held at the Nag^s^ead Tavern,
'Leadenhalt'Jlreety called the Amicable Association,
for the benefit of wido\^s and children, ^ftabliihed July 7^
•1767; which,' for no more than an annual payment of
iu^o guineas, not only, prom ifes the very annuity mcnti-
6ned above to the tuidctvs of members, but, if they leave
Ao widows^ to their cMldrm alfo 'till they arrive at the
age of fourteen years, beftdes 5 A towards putting thenrv

to apprenticeihips. ^There are, I am afraid, fcveral

more fuch wretched inftitutions in London ; befidt's
many fcattered every where in the country.

{b) 't'he London Annuity Society, inftead of promifmg
Annuities of 30/. to widows, it a member "lives feiwn
years, and of 40/. if he Xx^t^ fifteen years, now offer only
an advance to 30/. per ann. if a member furvives the
laft of thefe periods. This makes a very confiderable
amendment, but it is not fufficient ; for the dempnllia-
tions in this work, and efpecialty that in the noce»
page '399, may ^iffure them, that thcix contfiUutibns

D d will

402 SUPPLEMENT-

I wifli I could fpeak with the fame fatxs«
fadion of the afTociations in Londoh for pro*
riding for Old Age* It is true» f&ey are like«
wife endeavouring to reforni ; but in general,
as far as I know any thing of them» fo fed>ly
and ineffedually as to leave little room ta
doubt, but they will remain what they at pre-
fent undoubtedly are, Schembs of Fkaud
AND Theft.-— —Some of them, in conie**
quence of advancementSi fince the firft pub*
lication of this work, require now from thofii
who apply for admiflion higher contributioM
than thofe recited in the 4th SeA» Chap. IL
of this work. But they ought to remember^
that 'till all who have hitherto contribute^
too little, have either advanced their contri*
butions and paid the compenfation-monev
mentioned in page 1 1 6, or confented to fucn
deductions from their annuities, as ihall be
proportioned to the deficiencies in their pay-
ments : They ought, I fay, to remember^
that 'till tJbis is done, a reformation that
went even fo far as to require the Jul/ value$

will bear nothing beyonil the firft annuity they promife,
pr 20 A if a member lives one year ; and that as far as they
give any encouragement to exped more, they raife falie
and unjuft hopes. — The Laudable Society fer the benefit
of widows^ refolved, about two months ago, at a gene-
ral meeting, on a perfeA reformation. But I am juft
now informed, that through an unhappy infatuation^
they have lately revoked their refolution. I muft, how-
ever, flill hope, that the efforts of the wifer part of this
Ibcxety will fome time or Other meet with fuccefs,

of

SUP.P t £M £ NT* 463

of tlie 4tnAuitieS from aH\/iif/0r^ members^
would do thorn no great fervice.*— The truths
however^ is^ that reckoning intereft at 3I
fer cent^ their contributions are &i\\f in ge->
neral^ near a baff* below what they ought to
be (4). Is it poifihle then to fpeak of theft
focieties With too owch ieverity ? Can any
faetMTdleot pcrfbn fee them^ without con-
ccrA» going on with fchemes that have been
demonftrated to be infufiicient^ and iure to
«od in confuiion and calamity ?*^The Pro^
vidmt Society boafts, that it coniiils of laSo

(a) The true value of 30 /. per annum^ to be enjoyed
ftfter 50» bv a perfon now 40, is (reckoning intereft at
$ip€rcifii.) aj/. lo#. in annual payments beginning
immcdiatel/, Tbc value required by the Rational
Annuity Society, held at the Jntwerp Tavern, in
ThreadniidU'-Sireety is eight guineas in admiffion- moneys
and 4/. 8 1. in half-yiarfy payments* This rociety5 there<^
fbce, does not take half the value of the annuity it pro*
im£Bs ; and yet, 'Wiihjingular modejly^ it afiures the pub*
lie, that it is formed on a plan incontestably du-
KASLE.-^The WisTMiNsTEH Union Society of An*
ktiifaHtf^ held at the Standard Tavern, Leicffiir-Fitldsi
proofiifeS to a perfon, aged 30, an annuity of 25 /. for
life after 48, for 3 /• r6 s. per annum^ 'till 48, payable
quarterly* The true value is 9/. 10 j. per annum^ pay*
able quarterly* The value required by the fame fociety
at the age of 10, is 1 /. per annum. The true value is
2/. 13/. ^^r <?»»<<;;}.-— Every one who will calculate in
the manner dire£led in p. 112, &c. or in Queft. VI. p.
17, may make himfelf as fure of all this as he can be ot
imy thing.

I have here mentioned the two laft focieties particu-
larly, becaufe no notice has been taken of them in page
no, &c

Dd 2 mem-

404 SUPPLEMENT.

members ; and the Laudabk Society that it
pofieiTes an income of 9000 h ftt annum j-^
What is this but ihamelefsly boafting of the
numbers they hare deceived^ and the extent
five mifchief they are doing?— Some time
ago they might have pleaded ignorance i but
this is a plea they cannot now makc«

There ar6 four fodefies which I muft
except from thefe cenfures.— *The members
of the Friendly Society, the Consoli-
dated Society, and the Public Annui^
T ANT Society, convinced of the infufficiency
of their plan, have lately done themfelvcs
great honour by refolving to break up, and
returning undiminished the money they had
received. I have juft now learnt alfo, that
. the Society of London Annuitants, mention-
ed p. II o, is come to the fame reiblution ;
and its diiTolution, after fome ilruggks, final-
ly determined, in cpnfequence of the zeal
of many worthy and refpedable members,
particularly Mr. James Palmer, Mr. John
Charley, Mr. Thomas Marjham, Mr. TCbomas
Giffin, and the ingenious Mr. Henley, well
known to many in the philofophical world
for his fkill in EleSirical experiments*

It is neceflary I (hould add, in order to
prevent midakes, that the fociety for grant-
ing annuities increajing by Jurvivorjiap goes
on a plan different from any I have con-
fidercd, and the nature of which implies
fafetv.

Some

S U P l> L E M E N T. 405

Some thinks that thefe focieties may pro*
vide a proper iecurity for younger members^
and for ' all that fhall become annuitants in
more remote periods^ by preferving untouch*
ed all the ftock they fhall be pdleifed of^ at
the time when the payment of the annuities
fhall begin. But this is a great miftake.
An inadequate plan muft neceffarily benefit
fome bv robbing Wi&erj. For fome years
after tne commencement of the annuities^
the annual income of a ibciety muft exceed
its difburfements ; and all that time the firft
ttnnuitants will receive more than they ought
to receive^ at the expence of all that are to
come after them; nor is there a method
poffible of preventing this injuftice,— ^The
efFedt, in particular, of fuch a regulation as
that now mentioned, will only be^ that a
little will be fecured to annuitants in later
-periods, whereas otherwife they might have
had nothing. I fhould be too tedious, were
I to enter minutely inta the explanation of
this. The general reafon of it is, that by
paying too much to tht Jirfi annuitants, that
accumulation of ftock which the calculations
fuppofe (ftom Jurphis monies, while the an-
nuitants are increafing) would be prevented ;
and the adual ftock, in confequence of this,
be rendered fo much fmaller than it fhould
have been, as to leave but a fmall provifion
for the laft annuitants,

Pd 3 In

In (hotU In iiicb a iodety, the paynoentt
to annuiuots would become equal to its in<»
^ine, Jong, before their number roie . to ^
vwdmwn » and) therefore, if jtbe ibdety nnin-
t^ne4 its refolution not tp enter inbo it< i^Qok»
the annuities would, fro'm i^^ pfri(>dy de*
crea£$ contioually* 'till, at l«ft, tbey fpol; a^
much lower than they ought to havo been,
i« tbey wqre at firft J^igiftr^

VT ••

• . . . J .

I b«ive m«iitiQne(i i() tb^ introdn&km ft
thil workt p. |Ot the in|Qrpoj(ltioii..of tfaf
Jegiflaturct I doQ't know that this is u> b«
ejcpe£tfd« But th« foll^wiog fe^foo; ifew
to prove that it woul4 l>c propv, ihould #oy
of thcfe focieti«6 caiitio\ve nmch longer 4^
to the cftU^ of jufticejand hvunamtyr

Firft, They ape laying (as I have proved)
tl^ fouodation of much future mifchi«f i aa4
oo governipent ought to iee this with a can^
left eye.

Secondly. The principle by which they
are upheld is bafe and iniquitous. The./tr^
Jint members believe that the fcheipes they
are fupporting will laft their time, and that
tbey dial! be gainers ; and as for the injury
done to their fuccefTors, it is at a 4iftanc^>
and they care little about it.-^In conformity
to this principle, the founders of thefe fo-
cieties begin low i Jo low, aa not to require,
perhaps, z fourth or z fifth of tlie values of the

an-

SXTPTX E M E NT. 407

•nnuities diey jnomife. Afterwards j they
•drance gradsally, jufll as if they imaginedt
chat the value of the annuities was nothing
determinate^ but increafed with every in-*
creafe of the fodety, But> at no ignorance
can believe this, the true deiign appears to
be, to fcrm foon as largeLa fociety as pof-*
fible, by leading the unwary to endeavour to
be fbremoft in their applications, leaft the
advantage of getting in on the eafieft terms,
ihould be loft. — ^It is well known, that thefe
arts have fiicceeded wonderfully, and that»
in xoniequence of thetn, theie focieties now
con6ft of perfons who, for ikke.fame annuities,
iiiak& higher or lower payments according
to the tiflfte when they have been admitted ;
and the generality of whom, therefore, muft
know, that either oKMre than the values have
been required of the m^nbers laft admitted $
br if not, that they are themielves expedting
tbfffiderable annuities, for which they have
gfveh no valuable confideration, and which,
if paid them, muft be ftolen from the pock--
ets of fome of their fe]k>w->members^ What
icenes, therefore, of dijhonefty on the one
hand, and of unhappy credulity on the other,
are thcfc focieties ? \d).

Thirdly.

{a) If any perfon wants more information than I have
given him concerning tbefe focieties, or wifhes to fee a
more ample and minute account of the infufficicncy and
iniquity of their fchemes, he (houJd confult an ufeful

D d 4 work

4o8 SUTPLEMENT.

Thirdty. There are many lioheft men ii^
thefe focieties^ who having, ibicf mi£nibr?
Ifnation/ had the misfortuise to enter intQ
them, now repent, and would be glad.tp
withdraw* But, having made confideraUe
payments which they cannot get back, ikey
are forced to go on with further payments,
in order to avoid lofing all their former ones.-
Theie perfons wiih for affiftance from the
legiflatiire; and their cafes> I thlnk;^ require
affiftancc.

Fourthly. The fufferers by thefe aflbcia**
tions may, perhaps, ibme tioie or other, come
to be burdens on the public. This happea-r
^d in the cafe of the fufierers by the Cha-
ritable CoRPOKATjoN, for whofe relief
the parliament, in the year i733» granted a
lottery of half a million. The company of
Meecers are alfo now enjoying a parliamen-
|ary aid, in order to enaUe them to fidfil
their engagements to widows ; and it is well
known, what expences were brought on the
public by the bubbles in the Scuth-Jea year.
^— Ought not then the danger of fuch ex^
pences hereafter to be prevented ?

work publifhed fince the laft edition of this freatife, aii4
entitleid, Galcu^-ations ^ diducea from firft Principles^
in the mo/i familiar Manntr^ by plain Jlrithmettc^ for tbi Ufi
of the Societies injiitutidfor the Benefit of old Age ; intended a^
hn IntroduSlion to the Study of the D^&rine ofAnnuitieu By
a Member of one of the Societies.

Aftct

SUPPLEMENT. 409

Alter all. Perhaps the enforcing of an zGt

inade in the year 1720^ commonly called the

fivBBi.B A&, might be fufiicient to break

4die£5 fodeties : And I hope that the hcmeft

part of them, (hould they continue to be

overborn by nombers, will think, cither of

liaidng recoiuie to this ad, or cf applying

'by petition to ParUament^ which, when

their cafe is in this manner brouffht under

its ' cdgnmoce, will, moft probably, foon

give relief. J

; I will add, that it feemsto me, that were

thefe fodedes indeed formed on dorable'plans;

there would he reafon fdr fnbjefiing theni to

feme ftgttlattons; in all ' of them the anxmi-

<|es are to commence iSveral years before^Id

age. Such annuities, were they^to become

yery. common in a ftate, fnight have a bad

efie£t| by weakening the motives to induf-

try, and promoting diffipation and idlenefs;

r—I have: declared a high opinion of fome

inftitutions of this fort. Indeed no one can

think more highly of them, when their ob-

)cdL is the fupport of the deftitute widow;

br in any way the relief of unavoidable dr-^

ilrefs ; and, particularly, when they are de-

iBgned to enable the lower part of miankind,

to provide againft the wants and incapacities

of old age. I have propofed a plan of this

kind at the end of the third Sedt. Chap. IL

?nd I will here beg leave to recommend

another.

1

4itt $nTVPtEM E IN TTi

another^ whiclu I tfaioki were it currtedin-^
to execiatron, would bQ jvciy tift^uU I
mean, a plan for eftabliihing rARxs^H Atf-
MUKTlB&» kteiy pubUfliod. in a. pampblel^
entitled^ ui Fropifalfor tftablifinng.Life An^
mities in P^rtybes^ for, tie Benefit ^.. tbeJn^
dujirions F/xnr: Feinted for Mr. Whtte^^ ia
Fket^StrMt.^"^^* It is a^ comnon (4) obfet^
▼ation/' as the iogcaious aad publioj^iiited
sirriter. of this pamphlet ob^rvest. ^^that
^< the money annually raifed for. th& pcdri
^' anmanta to» at kafi^ a miUioo .a year;
'^ and that yet in many placet they, are
f^ but indifferently-* provided for. To make
^^.provifion for one's <old age is £> na?-
*' tural a piece of prudence, that it feooii
^< at £rft fight wondecf uU . that itihouldoot
be generally, pradifed*: by the labouring
poor, as it is alitioft uniVerially by per%
'^ fons in the higher piathsi of induflry x Nor
can their negligence in this . n&p^ be
accounted for».in any other way fa na***
turally^ as by afcribing it to their wanting
proper opportunities of employing iIk
money they might fave» in fome iafe and

€€
€€

€€

(a) The amount of the poor«rate for ooe year at th9

end of the reign of king Charles II. was 6659362 /• See

Davenanfs works. Vol. I. p. 38. The prices of the

means of fubfiftence have been finee doubled ; and when
this is confidered ; and alfo, that an increafe of parifli
poor muft be one effcd of the caufes that produce depo-
pulation y it will appear probable, that the obrervatioxi
above-mentioned does not exceed the truth.

*' cafy

$UP P L e M E NT. 4it

<^ etfy method thM would procure them a
«^ ittitabk advantage from it in the latter pe-^
^^ riods of their live$. They know» for the
«^ moft part, but little of the puUif funds^i
* and when it happeoa that they are ao*
'* quainted with them, the fmallnefs of the
f ' fums they would be entitled to receive, aa
<^ the intereft of the money they could af-*
^' ford to lay out in thera, is no encourage*
'^ ment to them to difpofe of it in that way^
!^ What inducement, for inftance, can it be
^< to a man who has faved ten pounds out
^ of his year's wages, to in vcft it in the pur*
** cha(i^ of 3 per €cnt. Bank annuities ^ to con*
^* iider that it -will produce him fix or ieven
<< ihiUinga -a year ? It. is b^t the wages of
•* three days labour.-~And if they lend their
ff- moa^ to tradesmen oC their acquaintance,
<< as ^ey fometimes do, it happens not un«
^* frequently that their creditor becomes a
*^* bankrupt, and the money they had trailed
<• him with is loft for ever ; which difcou-
<^ ragee others of them from faving their
*^ money at all, and makes them refolve to
f ^ fpend it in the enjoyment of prcfent plea-
'* fnre^ But if they faw an eafy method of
^* employing the money they could fpare, in
^^ fuch a manner as would procure them a
^* . confiderable income in return for it at fome
" future period of their lives, without any
^^ fuch hazard of loling it by another man's

** folly

1

4ia SUPPLEMENT.

€€
€€

folly or misfortune^ it n pr6bd>Ie they
would frequently embrace it : And dius a
^* diminution of the poor rate on the eftates
♦* of the rich, an increaie of prefent induftry
** ' and fobriety in the poor, and a more in-
•• dependent and comfortable fupport of theiAi
♦' in their old age, would be the happy con-
** fequcnces of fuch an eftablifhment. Now
** this might be effeded in the following
^^ method.

Firft, " Let the church-wardens and over-
'« fcers of every parifli be impowered, ty -aft
** of parliament, to grant life--annuities td
*^ fuch of the inhabitants of the pariih, aa
^ {ball be inclined to purchafe them, tocom-
•* mence at the end of one, two, or thrcd
^' ycard, or fuch other future period of timd
^< as the puFchafer ihall chufe, and to be paid
** out of the poor rates of the parish, fo thit
^' the lands and other property in the par^
^^ that is chargeable to the poor-rate, diaH
** be anfwerable for the payment of theife
**• annuitics,-*-This circumftance would give
♦^ thefe anniiities great credit with the poof
«* inhabitants, by fetting before them a fo-^
♦* lid and ample fecurity for the payment of
** them.

Secondly, *^ Let the annuities, thus grant*,
ed to the poor inhabitants, be fuch as arifi^
from a fuppofition that the intereft of mo-
^* ney is 3 per cent, or fomc higher rate of

" intereft^

€€

SUPPLEMENT. 41J

^^ interefty if the churchwardens and over-*
'^ feers of the poor think fit to make ufe of
'^ fuch higher intereft.

Thirdly^ ** But at the rate of 3 per cenf^
^ the purchafer ihould have a right to an an-
^* naity^ and the church-wardens and over-
«* feers of the poor ihould be compellable to
^ gtanf it.

Fourthly^ ** No annuity depending on one
^< life ihould exceed 20 A a year^

Piftiily^ '' No lefs fum than 5 L ihould
^ be allowed to be employed in the pur-
^' cfaaie of an annuity.-—— This is to avoid
^ intricacy and multiplicity in the accounts*

Sixthly^ ** An exad regiiter of thefe grants
«< ihould be kept^ by the church- wardens and
^* over£:ers of the poor^ in proper books for
^^ the purpofe, in which the grants ihould
^ be copied exadly^ and the copy of each
^ grant fubicribed by the perfon to whom it
** is granted. And this copy, in the regiiler-
^* book of the pariih, ihould be good evi-
^* dence- of the purchafer's right to the an*
** nuity, in cafe the original deed of grant to
<* the purchafer, which was delivered to
^* him at the time of the purchafe, ihould
♦* be afterwards loil.

Seventhly, ** The money thus paid to the
^ church-wardens and overfcers of the poor
^' for the purpofe of life-annuities, ihould
** be employed in the purchafe of 3 per cent.

" Bank-

4t4 S U P P t B W E N T;

#

<^ Bank-annuitiea ill the joint tkiroiti of all
*^ the church-wardtas 9nd ov^feers^ ttid by»
*^ them transferred at .the expiration of their
'.^ offices to their fucCcflbrSy and ib On to the
*'. next fuccelSbrs for dver, ib a$ tp b^ alwajrt^
the legal property of the church-wardei^
and oyerfeers of thfi poor ibr the time
being, in truil for the perfons who ihould
^^ be entitled to the ieveral iife-j^fiauities^
^^ granted in the manner above^mentioa^d f
^ and the intereft of tbil money (hould be
received every half year, and inirefted iit
the purchafe of more principal cdntiaaally^
ib as to make a perpetual fund for the
payment of the annuities, tie, &c. Defi-
cienirioi, if any ihouid ever happen^ to be
«• made good by the poor-rates, &c» &c*"

I hope I ihall be excttfed the length of
this Quotation. The particulars recited in it
are followed, by an account of the annuities
to which the payment of loA at the. age. c^
25, would entitle, after attaining to the age

^^3^> 35* 4^> 45» ^* ^^^ ^'^^ ^y ^ ^^
juft and clear explanation of the method of

calculating fuch annuities*

To the whole is added, a draught of an

A&. of Parliament for enabling pariih-officers

to grant fuch annuities, drawn up in confe-

quence of inftru£tions from fome members

of the Houfe of Commons, and particularly

one

4€
€€

€€
CC
C<
€€

tee * ^eotl^min of great eminence^ who has
£gDified an inteation of jbringing fuch a bill
into parliaaieot.

I ihafe no alterations, in this £:heiiie to
propefej that I think very material. .I,xe-
joioe to find that it is likely to be brought
under the confideration 6f the lqgiilature» I
will, however, jnft mention, that in order
to avoid all danger of checking induftry
among the poor, it would, perhaps, be right
to provide that the annuities fhall not com-
mence before the purchafer has compleated
the age of 50, 55 or 60 ? And alfo, that it
might be beft, that the annuities ihould be
made to increafe gradually with the in«
creafing infirmities of age, till they became
greateft at 65 or 70 years of age, when
their aid will be mofi: wanted ?

For inftance. Let the annuity begin with
I o /. for 5 years. At the end of 5 years, let
it rife to 20/. for five years more; and after
that let it be 30 /. for the whole remainder
of life. Let alfo every purchafer be allowed
to chufe at what age his annuity fhall com-
mence; and, as a further advantage, let it
be payable quarterly^ and let him be allow*
ed to purchafe 7, 4> ^9 &c- o^ the annuity,
juit as he (hall like or can beft afford.-— In
this way, perfons who are now young might
make an ample provifion for old age on very
<;afy and inviting terms.

a A re-

4i6 $\JPPttMtUt^

A refpedtable body of med in thid king^
dom, vrhofe fubfiftence too generally dc^
pends on the continuance of their capacities
of prefent ierVlctf^ hive^ for fome time, had
under coniideration a plan of this fort ; and
it fet of tables has been compofed for themi
As poffibly theie tables may be of fome ge^
fieral ufe^ I (hall beg leave to fnbjoin them^ '

f
/

TABLE

SUPPLEMENT: 417^-
T.A B L E I:^

Shewing the prcfcnt V^luc of an Annwity of 10 7;^
for five years J 2q/; for the next fuccccding five
y^ars; ^nd 30/. for the whol^ of jife after tert
years'; payable fuarierfy ; and ta eommcnce at
Fifty-five years of-age. >

lA^eof the
Porchafer.

*

acf

21

22

*3

24

'I
20

27

28'

29

30
31
32
33
34

3;
3'
33f
3«

39

40

4»
42

43
44

Value of the Annuity ia
one preXent PaymcAi.

./.

.38
40
42

44
46
48

51
53
56
.58
61

64

68

71
74

78
.81

85
89

94

98
103

109

114

121

128

Si

6

7
8

9
II

13

3

14
6

18

zi

t6

I

7

13

o

x6

12

9

M
16

4
o

8

y«lae of tKe annuity in j
antioal paynentsy to
bccontirfued 'till 55,
the I ft payment to be
made imiiiediately.

.2
.2

2

2

2

3
3
3

3
3
4
4

4

5

5
6

6

7

7
8

9
10

II

12

13
15

£ e

J.

-4

7 .
10

13

16

4
8

i8>

4
li

18

5

'3
I

ii

2 •

»3
6

o

o

o

3.
^3

_!.

TABLE

\

4i« S tr,P r t E W fil^T.

T^A^ Li: ir%

SKev^irtg tWe VkftnJs '6f an Anrt^ily oF td /. for five y«a«r J

20/. f<* the wxt&ccierfiftg'*fitk years; and 30/. for

• the whole bf «ft aftcf teW jWsirsj payajb^^ ^luarintf^

and to. cofAmence at SBrfr !^«% of* Ag6.

iWl'^^^

X- yr.ii

■'^ . > *•

.

A"p6

the Prfr-
cbftfer.

Valut of the Annuity in
, one pi^feat Payment.

,

20

\22

. as

'^^
16

•29
ao

.52

A 33

4

?
6

37

»8

,39
40

I^l

42

43

44

46

.47

4«
49
50

;.

^\

rib«<

t

« •

22

23

•-2.;

: 26

r 27
28

r.3*

?.33

35
36

38

40

46

48

S'

53
56

61

64

. 68

. 7*

' 77
81

S6

96

ro2

■*■»

Valuebl* the Annuity in
aiuidiil Pa^mentSf to
he continued tUl the
Age of 60, th6 titfi
^aytltfcht «> fe ttfade
immediatdly.

w

I

2'

»3

.4.
18

12

%

'a-
o

a

5
q

to
p

I>

o

Id

•o

10

^ o

y*

1

/.

I
I
I
I
I
•1

I
1

2

a
a
a

a
a

3
3
3
3
4
4
5
5

I

7
8

9

9
.11

12

I

10

o •

3

6

9
li

»f

I

'9
S

d

a

is

*4

Id

16
a

lO'

i

i

I

t&sLe

S U P PL fe M E N T; 41^

TABLE III.

Shewing the Values of an Annuity of 10 /. for five years ;
20 /. for the next fucceeding five years ; and 3Q /. for
the whole of life after ten years ; payable quOirttrly^ and
to commence at Sixty-five years of age.

» « V

Value of the Aanaity in

Age .of
the Pur^

Valtie bf the Annuity ia

annual Pajmsenti, to
be coicinued till the

chafer.

one piefcnt PaynkejDt.

Age .6 5, and to begin
immediately.

/. i.

/. X. d.

20

12

: 4

: 13

:

21

12

: 18

: «3

' 9

22

•3

: .12

' 14

: 6

*3

H

: e,

5 '5

: 6

2+

IS

\ i

i 16

: 6

25

>5

\ 16

;

: 17

: 6

26

16

' n

:

: 18

: 6

27

17 '

10

:

. '9

( 6

28

18 :

5 7

: 6

*9

19 :

5

i 2 :

;

30

20 : 3

3 J

; 6

31

21 t 5

5 :

:

■32

22 :

7

7 :

33

13 1

10

9 i o|

3+

24 :

: 13

: >i :

35

25 J

16

13 :

36

27 :

! *5 ;

37

28 :

4

17 5

; 6

38

29 I 9-

2 •

39

30 :

H .

2 :

. 3 :

40

3*- 1

; ^

2 :

6 :

4«

3+ -

2

10 :

4»

36 ;

2

H :

43

38 :

2

18 :

1

44

40 :

3 :

3 J

\

4|

42 :

5

3 :

8 ;

;

46

44 ■

»>

3 :

: H V

;

47

47 J

9

4 :

I ^

48

50 J

• 3

4 :

9 J

49

53 :

4 :

; IS \

;

50

55 '

: 18

5 :

; 7 J

;

5t

59 '

6 .

; 1

' 33

62 ;

10

6 \

: >5. -

\

67 :

7 \

; 10 C

$4

72 ;

^ ;

; 10 :

.-.55 ,.

77 :

12

. ?„'

17 :

£ e 2

Thcff

420 SUPPLEMENT,

Thcfe Tables have been ca]cul|ted by the rules in
Qucft. VI. page 17, 18, &c. The probabilities of life
have been taken from Table IV. page 323 : And the in-
tcrcft of money reckoned at ^per cent.

It is proper, in order to prevent all danger of miftakes,
to add, that the values in each of the fccond and third
columns of thefe Tables, are the whole values. That is,
The values in the fecond column of every Table fuppofe
the payments in the third column excufed. And, in like
manner, the values hi the third column fuppofe the pay-
ments in the fecond excufed.

TABLSs

SUPPLEMENT. 421

TABLE IV. (a)

Shewing the Probabilities of Life in the Diftrifl of Vauo,
Switzerland, formed from the Regifters of 43 Pa-
ji(hes, given by Mr. Murety in the Firft Part of the
B£RN Memoirs for the Year/ j 766.

Ag«.

Li?ing

iJeCT* ;

t

Age.

LiTJng

Decy.

Age;

Living

Deer.

1000

189

3«

558

5

62

286

12

I

811

46

3*

553

5

63

274

12

2

765

30

33

548

4

64

262

12

3

73S

23

34

544

• 5

4

7"5

«4

—

65

250

H

• S

701

«3

11

539
^33

6
6

66
67

236

220

16

18

6

688

If

37

527

7

68

202

18

7

677

10

38

520

7

69

184

16

8

667

8

39

5«3

7

9

659

6

70"

168

*5

40

506

6

7'

153

>3

ro

^M

S

4>

500

6

7»

140

11

II

648

s

42 .

494

6

73

129

10

12

643

4

43

488

6

74

119

10

«3

639

4

44

482

6

«4

635

4

7|

109

II

45

476

7

76

98

>3

»5

63,

5

46

469

8

■

77

85

H

16

626

4

47

461

10

78

7«

•3

«7

622

4

48

45«

10

79

58

12

18

618

4

49

441

10

19

614

4

80

46

10

— —

—

50

43 i

9

81

36

7

20

610

4

S'

422

8

82

29

5

21

606

4

52

4»4

8

83

24

4

22

602

S

S3

406

9

84

20

3

^3

597

5

54

397

9

24

592

5

H

»7

3

1

55

388

II

86

H

3

25

587

5

56

377

'1

87.

11

2

26

582

5

57

364

16

)?8

9

2

^7

^77

5

58

348

'7

89

7

2

28

572

5

59

33>

>7

29

567

4

^0

3H

>S

90

5

I

30

563,

5

61

299

>3

(a) All the Billsy from which thii and the following Tables are

tmed, give the Rumbert dying under i as well as under a years {
L injihe nuphersdying under i, are included, in the country
^ariibiii UrantUaburgtAi^JxBsrliM^ all the ilill-borns. All the InlU
alio give the numbers dying in crery period of five years^

422 supplement;

TABLE V.

Shewing the Probabilities of Life in a Country Parifh in '
Brandenburg, formed from the Bills for 50 Years,
from 17 10 to 1759, as ^iven by Mr. Susmilch, in
bis Gottlichi Orduung, page 43.

Shewing tbe Prot^abilicie$ of ]Lif<; in Ji;hf fariflbi)f

* l^pLy-CaoaSt near SaRiwswjRy, /grmed trom

a R^giftcr l<;cpc by the Key. Mr, G^fiicb, for

20 years, from 1750 to 17 JQ- '^c ragp 1^2^

^WK.

p

1

2

3

m ^ '^

5
6

7
8

JO

n

12

14

i5
16

17
18

23

24.

25"

*7
?8

29.

30

Lifhig.

Hqoo
882
762

717
682

P«cr, j

618
604

595

599

585
581

577
573

569

565
560

555
5

'io

5^5

539
532

is? 5
518

512
506

501

496.

49 »

l8?|

178
^a

45
35

-iiJ

23
18

14

9
6

4

4
4

4

4

5

5

/•

3

6

7

7

7
6

5

5
5
5

^■^

3?
33

34

35

37

3S
|9 1

40

41

4f
43
44

45
46

4.7
48

49

Uvtn

£

Deer.

481
.47(^

47 J

466

460

45-i-

447
440

433

426
418
410
401

393

50
51
52

53
5±_

55
56

57
5§
|9

386

379
372

3^5

359

l-

60
61

^rmm

353
347
340

333

3^
3^0

301

292]

«83

*73
263

5

5

I

7
7

?'•
7

8
8

9
8

7

7

7

7
6

6'

9

9

9
10

10

lO

11^
62

72
73

75

76
77
78

80
81

8?

«3
84

8-

86

87

89.
90

91
92

" , ■ ' ■ ■ " ■»

Age,- U»in(!.f Deer. I
t^J - " * — ' > ' J

B2 2,2 10

6
7

7

7
8

j3
243
233

ix>

10

323

^i3)ip;

.2Xi5

^93
,182

10 1]

i7.>

151
142

134!

T

IP

8

.81

ii6
119
112
105

98

7

7

7

7
8

90
8<

7«
61

51

9 J

lO

10
10
10

'■■■■IP'

41

3-

^4

17
II

7
5

4I

9

8

7
6

4

2
I

I

t

ipf

S-U.PiP L EJl'E.N T.
T k BLtB VII.

Shewing the ProbibiHtiK of Life at Viebha'
formed from'jhe^ii&frfEighrye^rs, ai given
by Mr SoSMiicB, in his Gsillicbi Ordniam.

• Page 32, Tables. '. ^ ' '. '

Ar-

■JTLBt.

D^.

gh

o

■495

I

.8'3

107

i

706

Si

3

645

4«

4

599

33

S

566

3°

.6

•536

20

7

516

ii

-8

505

9

4-

496

7

lO

-489

•6

II

483

5

12

478

'3

473

6

■4

467

6

■?

461

■6

i6

>J55

7

■7

448

6

i8

442

6

'9

_t36

6

2a

430

■5

21

425

5

22

420

5

23

415

6

5i^

409

6

25

403

6

26

397

6

27

39^

7

28

381

7

29

377

7

e-

370

6

4»^

Li-i.1.

DMr.

62

129

-T

«3

123

7

64.

116

7

65

109

8

66

IQl

8

67

93

8

<8

85

7

69

78

7

7°

7>

6

7'

65

5

7'

60

5

73

■55

4

Zi.

5'

4

75

47

5

76

42

5

77

37

5

78

32

5

79

27

4

80

23

3'

81

20

2

82

'9

2

83

16

2

84

■4

2

85

12

2

86

ID

2

87

8

2

88

6

2

89_

4

I

90

3

1

91

2

1

92

I

I

425

SUPPLE MEN T:
TABLE VIII.

Shewing the Probabilities of Life at Bbrlin^i formed
from the Bills for Four Years, from 1752 to 1755,
given by Mr. Susmilch (<?}, in bis Gottlicbi Ordnungi^
Vol. IL page 37, Tables.

Ag».

LiTiaf

D«n.

Age«

Liviog

Decri.

Age.

Ifiving

Deer.

1427

5*4

33

361

7

ii

112

6

I

903

*S'

34

354

7

66

106

7

2

75*

61

67

99

7

3

^91

73

3S

347

8

68

92

6

4

618

4J

36

37

339

330

9

10

iL

86

6

1

573

21

38

320

10

70

80

6

6

55?

>5

39

310

10

7»

74

6

7

536

«3

72

68

6

8

5*3

9

40

300

10

73

62

9

S>+

7

4«

290

9

74

57

■

4*

281

8

i

10

507

5

43

^l^

7

75

52

II

502

4

44

266

7

76

47

IS

498

4

77

42

13

494

4

^i

259

7

78

37

• J

14

490

4

46

15

252

2+5

7

7

79

3»

......

»5

486

4

238

7

80

28

16

482

5

49

*3»

7

8t

24

17

477

5

•—

82

21

2

18

472

1

50

224

7

83

\}

2

>9

467

S«

217

7

84

2

" "

—

5«

210

7

■ ' ■ ■

ao

461

6

53

203

8

!l

«5

2

ai

455

6

54

«95

8

86

»3

2

zt

449

6

87

II

2

23

443

7

55

187

8

88

9

2

«4

436

8

56

5Z

"79
'7*

8
8

89

7

1

»c

428

9

58

163

9

90

6

26

421

9

59

»54

9

9'

5

»7

412

9

92

4

28

403

9

60

145

8

93

3

39

394

9

61

137

7

94

2

62

130

6

■

■ 30

385

9

63

124

6

3»

376 8

64

118

6

. 3»

368 7

(fl) This writer has alfo given the bills of the pari(h of
6t. Peter* s at BBaLiN, for 24 years; and a Table formed from
thcni» agrees nearly with thu.

The

4tik SUPPLEMENT.

The following fads eamc to my know*-
ledge too late to be jnferted in their proper
places^ They furnifh additional evidenc<r

for foroe of the QhfervAtions I hM?e made ^

find^ therefore^ I have chofen to introduce
pn account of them h^vc^ father th^n en-r
tirely omit theqif

An exa<ft account wa) taken in Augoft^
1772, by the defirc of the EJarl of Sbelburne^
pf the number of families^ and of inhabit
Itapts in Calne, a manufadturing towi^ ii|
Wiltshire,— The number of married perfpn|
pnd heads of families was 1102; (m Jin^lf
ficads of families, 241 ; of children^ ^^H?
pf lodgers and fervants^ 510 ; of families^
776 i and of inhabitants or all ages ai)d con«p
'ditionsj exclpfive of 58 in the poor^houfei
3467 ; or near 4$ to ^ family.

About the fame time an eyadi: account
viras thken alfo of the town and parish of
Wycombe in Buckmgbamjhire^ and th^
pumber of families in the town was foi^nd
to be 432; and of inhabitantSt exclu0ve of
46 in the poor-houfe, 21 52, or ^' to a fan

The numbers htnt at Berlin, duiing thf 4 yearn «bovemen^
ttoned, were, P^leSt 92x9 i femc4es^ ^74-3 » ^^ ^l to. 2C.

The numbers |hat liied under a year$ oi*«ge, were, MMleit 3 1 TS 1;
femaUs^ 2623 ; or 7 to 6.

^be nambers thitt died upwards of 80 jeirs of age* were,
maUsi 13s \.femaUii 215 ; or <; to 8.

The numbers that died betw'ieea 91 and I05» were* pi^h 211

mily.

supplement: 4)17.

pify. In that part of the pariih which lies
in die country, were 6H familie5| ^^d 309
inhabitants, or 4! to 2i family.

At Altringham, a market-town ia
Cheilure, according to an accurate furvejr
made in July laft, the number of houfes wai
348, of inhabitants, 1029 ; or 4^^ to ihoiife.

St. MichaeV^^ a fmaU parifh in the cen«^
ter of the towp of Chestkr, contains, ac-
pording to a very txzdi account taken under
the diredion of Dr. Haygarth, %\t males»
372 females, 166 married pcrfons, 41 wi**
Hows, 21 widowers, 137 children under 15
years of age, 1 5 1 families, 1 27 houfes, and
6i8 inhabitants, of 4tV to a family ^ and 4^
to a houfe.

At Birmingham, in the year 1700,

The inhabitants were 15032

Xhe houfes r-r r— • 2504, or 6 to a boufe^

In 1750, ,

The inhabitants were 2 '2688

» • » . . %j

The boufe^ r?: r— 4 1 70, or 5 A to a hatfe^

In 1770,
The /^^Zfj" were -^ 15363
The females —5: -—15441

Total of Inhabitfjnts in 1770—730804

Houfes ^. ^ ~- 6025, or 5-J
to a houfe.

428 SU PP L EM E N T-

We may lee, in this account^ the progrefir
of luxury at Birmingham ; the houfes there
having increafed fo much fafler than the in^
habitants, that 600 houfes now contain no
more people than 511 contained 70 years
ago.

In a hundred fmall towns and parishes in
^e generality of Rouen, 26 in the gene-^
rality of Lyons, and 16 in the generality of
AuvERGNE in France, the married men
and widowers were a few years ago 199 16;
the married women and widows 22494; the
males 478 1 7 ; the females 5 11 8 5 ; the inha*
bitants of all ages and conditions 99002 ;
the families, 24910, or nearly 4 to a family.
See Recberches fur la Populatioriy par M.
MeiTance, page 8, 26, 62.

Similar accounts of Norwich^ Manchejier^
Leeds^ Sbrewjbury^ Nortbamftotiy Newbury^
Rome^ the diftriiS of Faud in Switzerland^
Sec. &CC. may be found in page 183, &c, and
the beginning of the Supplement.

At Gainsbrough, in Lincolnjhire^ a re-
gifter has been kept for many years of the
cbrifienings^ weddings^ and burials^ in which
are particularly diftinguifhed the numbers of
each fex dying at every age in every month.
I have lately obtained, through the ailiflance
of a friend who lives in this town, a copy
of this regifter for 20 years back, or from
J 752 to 1771.— The annual medium of

chrlften*

S U P P L E M E N T^ 429

chriftenings during this period^ including all
among diSenters, has been 1 26 ; of wed«
dings, 34; of burials, 10^.— -The weddings
in fummer (July, Auguft, September) have
been 130. In, winter (December, January,
March) 144. In autumn, 188^. Fn fpring,

218. The cbrijitnings in fummer (June,

July, Auguft, and September)- have be^n
779. In winter (December, January, Fc-
bruary, March) ;8 1 1 The Burials in the

fame four fummer months, h'ave been 590.
In the four winter months, 765. The mcr--
tality d^ fummer t therefore, in this town, is
lefs than the mortality of winter^ in the pro-
portion of 4<3 to 52. See the note in p. 3714
The burials in April and May have been
390. In OStober and November y 345. — The
chriftenings in April and May have been 427«
In OSiober and November y 410

>

;•!

Died

4^ itlPPLEKiEJ^t;

At GAINSfeRbUCSH,

" i

Died under 20

Between zo afid 25

^5 dnd

30 and

35 *^^

40 ^nd

45 and
59 ^^d
$} and
to dnd'
65 and
^b and
^5 and

3^

3S
40

45
50

55

60

65

70

80 and 101

«5

. IS

A7

SZ

. i1
43
SI

femalei.
ft »•

485

Z9

411

41

35

3^

25
48

49

73

50

5»

30

49

] Of all ages in 20 years j 10^4 ) 1 046

lOIO
60.

95

loi

130

93
10;^

61

.81

£oyo

According to this Tabic, one*half of all
that are chriftened live to 2i years of age;
and 81 of 2070, that is i in 25 1» live to
80^ of whom the major part, in the propor*
tion of 49 to 32^ are females.

The town and parifh of Gainsbrough
coniift of 920 houfes; of which 161 are
houfes in the hamlets and country round thc;^
town*

A TABLE

A TABLE fhewing the ndmbers
tvho have died at all ages for i o years, in
two towns, and 13 parifhes, in the generali-
ties of Lyon and Rouen in France. Taken
from Recbercbes fur la Population^ &c. par
M. Mejfance^

Died Odder 5
From 5 to lo
10 to
20 to
30 to
40 to
50 to
60 to
70 to
80 to

90 to lOO-'— -

4884

FINIS.

\ 9 •

I